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Lesson 10-1 Simplifying Algebraic Expressions Lesson 10-2 Solving Two-Step Equations Lesson 10-3 Writing Two-Step Equations Lesson 10-4 Sequences Lesson 10-5 Solving Equations with Variables on Each Side Lesson 10-6 Problem-Solving Investigation: Guess and Check Lesson 10-7 Inequalities Chapter Menu

Five-Minute Check (over Chapter 9) Main Idea and Vocabulary Targeted TEKS Example 1: Write Expressions With Addition Example 2: Write Expressions With Addition Example 3: Write Expressions With Subtraction Example 4: Write Expressions With Subtraction Example 5: Identify Parts of an Expression Example 6: Simplify Algebraic Expressions Example 7: Simplify Algebraic Expressions Example 8: Real-World Example Lesson 1 Menu

Use the Distributive Property to simplify algebraic expressions. like terms Look alike! – Same vars! Constant A number w/o a variable simplest form All like terms combined simplifying the expression Combining all the like terms equivalent expressions Expressions that are equal no matter what X is Term A “part” of an Alg. Expression separated by + or - Coefficient The number in front of a variable Lesson 1 MI/Vocab

a (b + c) = ab + ac NOTES Quick Review Session Distributive Property I can only combine things in math that ????? LOOK ALIKE!!!!!!! In Algebra, if things LOOK ALIKE, we call them “like terms.” The Distributive Property Lesson 1 TEKS

Write Expressions With Addition Use the Distributive Property to rewrite 3(x + 5). 3(x + 5) = 3(x) + 3(5) = 3x + 15 Simplify. Answer: 3x + 15 Lesson 1 Ex1

Use the Distributive Property to rewrite 2(x + 6). A. x + 8 B. x + 12 C. 2x + 6 D. 2x + 12 A B C D Lesson 1 CYP1

Write Expressions With Addition Use the Distributive Property to rewrite (a + 4)7. (a + 4)7 = a ● 7 + 4 ●7 = 7a + 28 Simplify. Answer: 7a + 28 Lesson 1 Ex2

Use the Distributive Property to rewrite (a + 6)3. A. 3a + 27 B. 3a + 18 C. 3a + 9 D. a + 18 A B C D Lesson 1 CYP2

Write Expressions With Subtraction Use the Distributive Property to rewrite (q – 3)9. (q – 3)9 = [q + (–3)]9 Rewrite q – 3 as q + (–3). = (q)9 + (–3)9 Distributive Property = 9q + (–27) Simplify. = 9q – 27 Definition of subtraction Answer: 9q – 27 Lesson 1 Ex3

Use the Distributive Property to rewrite (q – 2)8. A. q – 16 B. q – 10 C. 8q – 16 D. 8q – 10 A B C D Lesson 1 CYP3

Write Expressions With Subtraction Use the Distributive Property to rewrite –3(z – 7). –3(z – 7) = –3[z + (–7)] Rewrite z – 7 as z + (–7). = –3(z) + (–3)(–7) Distributive Property = –3z + 21 Simplify. Answer: –3z + 21 Lesson 1 Ex4

Use the Distributive Property to rewrite –2(z – 4). A. –2z + 8 B. –2z – 8 C. –2z – 4 D. –2z A B C D Lesson 1 CYP4

Identify Parts of an Expression Identify the terms, like terms, coefficients, and constants in 3x – 5 + 2x – x. 3x – 5 + 2x – x = 3x + (–5) + 2x + (–x) Definition of subtraction = 3x + (–5) + 2x + (–1x) Identity Property; –x = –1x Answer: The terms are 3x, –5, 2x, and –x. The like terms are 3x, 2x, and –x. The coefficients are 3, 2, and –1. The constant is –5. Lesson 1 Ex5

Identify the terms, like terms, coefficients, and constants in 6x – 2 + x – 4x. Answer: The terms are 6x, –2, x, and –4x. The like terms are 6x, x, and –4x. The coefficients are 6, 1, and –4. The constant is –2. Lesson 1 CYP5

Simplify Algebraic Expressions Simplify the expression 6n – n. 6n – n are like terms. 6n – n = 6n – 1n Identity Property; n = 1n = (6 – 1)n Distributive Property = 5n Simplify. Answer: 5n Lesson 1 Ex6

Simplify the expression 7n + n. A. 10n B. 8n C. 7n D. 6n A B C D Lesson 1 CYP6

Simplify Algebraic Expressions Simplify 8z + z – 5 – 9z + 2. 8z, z, and –9z are like terms. –5 and 2 are also like terms. 8z + z – 5 – 9z + 2 = 8z + z + (–5) + (–9z) + 2 Definition of subtraction = 8z + z + (–9z) + (–5) + 2 Commutative Property = [8 + 1+ (–9)]z + [(–5) + 2] Distributive Property = 0z + (–3) or –3 Simplify. Answer: –3 Lesson 1 Ex7

Simplify 6z + z – 2 – 8z + 2. A. –z B. –z + 2 C. z –1 D. –2z A B C D Lesson 1 CYP7

Words $5 each for adults and $3 each for the same number of children THEATER Tickets for the school play cost $5 for adults and $3 for children. A family has the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets. Words $5 each for adults and $3 each for the same number of children Variable Let x represent the number of adults or children. Expression 5 ● x + 3 ● x Lesson 1 Ex8

Simplify the expression. 5x + 3x = (5 + 3)x Distributive Property = 8x Simplify. Answer: The expression $8x represents the total amount of money spent on tickets. Lesson 1 Ex8

MUSEUM Tickets for the museum cost $10 for adults and $7 MUSEUM Tickets for the museum cost $10 for adults and $7.50 for children. A group of people have the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets to the museum. A. $2.50x B. $7.50x C. $15.50x D. $17.50x A B C D Lesson 1 CYP8

End of Lesson 1

Five-Minute Check (over Lesson 10-1) Main Idea and Vocabulary Targeted TEKS Example 1: Solve Two-Step Equations Example 2: Solve Two-Step Equations Example 3: Equations with Negative Coefficients Example 4: Combine Like Terms First Lesson 2 Menu

Solve two-step equations. Contains TWO operations that need to be “undone” Lesson 2 MI/Vocab

BrainPop: Two-Step Equations NOTES The Goal of solving EVERY algebra equation is to GET THE VARIABLE BY ITSELF!!! I can only combine things in math that ???? To PUT SOMETHING TOGETHER, you follow the directions. In math, to put an expression together, we used a specific order of operations. PEMDAS If you want to take something APART you REVERSE the directions. To solve Algebra equations, REVERSE PEMDAS SADMEP BrainPop: Two-Step Equations Lesson 2 TEKS

Solve Two-Step Equations Solve 5x + 1 = 26. Method 1 Use a model. Remove a 1-tile from the mat. Lesson 2 Ex1

Solve Two-Step Equations Separate the remaining tiles into 5 equal groups. There are 5 tiles in each group. Lesson 2 Ex1

Solve Two-Step Equations Method 2 Use Symbols Use the Subtraction Property of Equality. Write the equation. Subtract 1 from each side. Lesson 2 Ex1

BrainPop: Two-Step Equations Solve Two-Step Equations Use the Division Property of Equality. Divide each side by 5. Simplify. Answer: The solution is 5. BrainPop: Two-Step Equations Lesson 2 Ex1

Solve 3x + 2 = 20. A. 6 B. 8 C. 9 D. 12 A B C D Lesson 2 CYP1

Solve Two-Step Equations Write the equation. Subtract 2 from each side. Simplify. Multiply each side by 3. Simplify. Answer: The solution is –18. Lesson 2 Ex2

A. 14 B. 8 C. –26 D. –35 A B C D Lesson 2 CYP2

Equations with Negative Coefficients Write the equation. Definition of subtraction Subtract 8 from each side. Simplify. Divide each side by –3. Simplify. Answer: The solution is –2. Lesson 2 Ex3

Solve 5 – 2x = 11. A. –3 B. –1 C. 2 D. 5 A B C D Lesson 2 CYP3

Combine Like Terms First Write the equation. Identity Property; –k = –1k Combine like terms; –1k + 3k = (–1 + 3)k or 2k. Add 2 to each side. Simplify. Divide each side by 2. Simplify. Lesson 2 Ex4

Combine Like Terms First Check 14 = –k + 3k – 2 Write the equation. 14 = –8 + 3(8) – 2 Replace k with 8. ? 14 = –8 + 24 – 2 Multiply. ? 14 = 14 The statement is true.  Answer: The solution is 8. Lesson 2 Ex4

Solve 10 = –n + 4n –5. A. 3 B. 5 C. 8 D. 10 A B C D Lesson 2 CYP4

End of Lesson 2

Five-Minute Check (over Lesson 10-2) Main Idea Targeted TEKS Example 1: Translate Sentences into Equations Example 2: Translate Sentences into Equations Example 3: Translate Sentences into Equations Example 4: Real-World Example Example 5: Real-World Example Lesson 3 Menu

Write two-step equations that represent real-life situations. Lesson 3 MI/Vocab

There are 3 steps to follow: Read problem and highlight KEY words. CONVERTING ENGLISH SENTENCES TO MATH SENTENCES! There are 3 steps to follow: Read problem and highlight KEY words. Define variable (What part is likely to change OR What do I not know?) Write Math sentence left to Right (Be careful with Subtraction!.) Lesson 3 TEKS

Looks for the words like: is, was, total EQUALS Notes – CONT. Looks for the words like: is, was, total EQUALS Less than, decreased, reduced, SUBTRACTION - BE CAREFUL! Divided, spread over, “per”, quotient DIVISION More than, increased, greater than, plus ADDITION Times, Of MULTIPLICATION Lesson 3 TEKS

Translate Sentences into Equations Translate three more than half a number is 15 into an equation. Answer: Lesson 3 Ex1

Translate five more than one-third a number is 7 into an equation. C. D. A B C D Lesson 3 CYP1

Translate Sentences into Equations Translate nineteen is two more than five times a number into an equation. Answer: 19 = 5n + 2 Lesson 3 Ex2

Translate fifteen is three more than six times a number into an equation. B. 15 = 6n + 3 C. 15 = 3(n + 6) D. 15 = 6(n + 3) A B C D Lesson 3 CYP2

Translate Sentences into Equations Translate eight less than twice a number is –35 into an equation. Answer: 2n – 8 = –35 Lesson 3 Ex3

Translate six less than three times a number is –22 into an equation. B. 6(n – 3) = –22 C. 3n – 6 = –22 D. 6n – 3 = –22 A B C D Lesson 3 CYP3

Words $3.50 plus $2 per mile equals $11.50. TRANSPORTATION A taxi ride costs $3.50 plus $2 for each mile traveled. If Jan pays $11.50 for the ride, how many miles did she travel? Words $3.50 plus $2 per mile equals $11.50. Variable Let m represent the number of miles driven. Equation 3.50 + 2m = 11.50 Lesson 3 Ex4

3.50 – 3.50 + 2m = 11.50 – 3.50 Subtract 3.50 from each side 3.50 + 2m = 11.50 Write the equation. 3.50 – 3.50 + 2m = 11.50 – 3.50 Subtract 3.50 from each side 2m = 8 Simplify. Divide each side by 2. Simplify. Answer: Jan traveled 4 miles. Lesson 3 Ex4

TRANSPORTATION A rental car costs $100 plus $0 TRANSPORTATION A rental car costs $100 plus $0.25 for each mile traveled. If Kaya pays $162.50 for the car, how many miles did she travel? A. 200 miles B. 250 miles C. 300 miles D. 325 miles A B C D Lesson 3 CYP4

Words Your friend’s dinner plus your dinner equals $33. DINING You and your friend spent a total of $33 for dinner. Your dinner cost $5 less than your friend’s. How much did you spend for dinner? Words Your friend’s dinner plus your dinner equals $33. Variable Let f represent the cost of your friend’s dinner. Equation f + f – 5 = 33 Lesson 3 Ex5

f + f – 5 = 33 Write the equation. 2f – 5 = 3 Combine like terms. 2f – 5 + 5 = 33 + 5 Add 5 to each side. 2f = 38 Simplify. Divide each side by 2. f = 19 Simplify. Answer: Your friend spent $19 on dinner. So you spent $19 – $5, or $14, on dinner. Lesson 3 Ex5

DINING You and your friend spent a total of $48 for dinner DINING You and your friend spent a total of $48 for dinner. Your dinner cost $4 more than your friend’s. How much did you spend for dinner? A. $22 B. $26 C. $28 D. $30 A B C D Lesson 3 CYP5

End of Lesson 3

Five-Minute Check (over Lesson 10-3) Main Idea and Vocabulary Targeted TEKS Example 1: Identify Arithmetic Sequences Example 2: Describe an Arithmetic Sequence Example 3: Real-World Example Example 4: Test Example Lesson 4 Menu

Write algebraic expressions to determine any term in an arithmetic sequence. An ordered list of numbers Term A specific number in a sequence common difference The difference between EVERY term is the SAME arithmetic sequence Where the terms all have a common difference Lesson 4 MI/Vocab

To Identify Arithmetic Sequences NOTES To Identify Arithmetic Sequences Look for a pattern that has a common difference If one exists, the sequence is arithmetic Ex: 15, 13, 11, 9, 7, …. To find the “rule” that describes a sequence Write the terms on top of the sequence number (1,2,3…) Find the “common difference.” Write down common difference followed by the variable Find out how much you need to ADD or SUBTRACT to get to the first term. Check your rule for the rest of the terms -2 -2 -2 -2 Lesson 4 TEKS

Identify Arithmetic Sequences State whether the sequence 23, 15, 7, –1, –9, … is arithmetic. If it is, state the common difference. Write the next three terms of the sequence. 23, 15, 7, –1, –9 Notice that 15 – 23 = –8, 7 – 15 = –8, and so on. –8 Answer: The terms have a common difference of –8, so the sequence is arithmetic. Continue the pattern to find the next three terms. –9, –17, –25, –33 –8 Answer: The next three terms are –17, –25, and –33. Lesson 4 Ex1

Answer: arithmetic; –2; 19, 17, 15 State whether the sequence 29, 27, 25, 23, 21, … is arithmetic. If it is, state the common difference. Write the next three terms of the sequence. Answer: arithmetic; –2; 19, 17, 15 Lesson 4 CYP1

Describe an Arithmetic Sequence Write an expression that can be used to find the nth term of the sequence 0.6, 1.2, 1.8, 2.4, …. Then write the next three terms of the sequence. Use a table to examine the sequence. The terms have a common difference of 0.6. Also, each term is 0.6 times its term number. Answer: An expression that can be used to find the nth term is 0.6n. The next three terms are 0.6(5) or 3, 0.6(6) or 3.6, and 0.6(7) or 4.2. Lesson 4 Ex2

Write an expression that can be used to find the nth term of the sequence 1.5, 3, 4.5, 6, …. Then write the next three terms. Answer: 1.5n; 7.5, 9, 10.5 Lesson 4 CYP2

TRANSPORTATION This arithmetic sequence shows the cost of a taxi ride for 1, 2, 3, and 4 miles. What would be the cost of a 9-mile ride? The common difference between the costs is 1.75. This implies that the expression for the nth mile is 1.75n. Compare each cost to the value of 1.75n for each number of miles. Lesson 4 Ex3

Each cost is 3. 50 more than 1. 75n. So, the expression 1. 75n + 3 Each cost is 3.50 more than 1.75n. So, the expression 1.75n + 3.50 is the cost of a taxi ride for n miles. To find the cost of a 9-mile ride, let c represent the cost. Then write and solve an equation for n = 9. Lesson 4 Ex3

c = 1.75n + 3.50 Write the equation. c = 1.75(9) + 3.50 Replace n with 9. c = 15.75 + 3.50 or 19.25 Simplify. Answer: It would cost $19.25 for a 9-mile taxi ride. Lesson 4 Ex3

TRANSPORTATION This arithmetic sequence shows the cost of a taxi ride for 1, 2, 3, and 4 miles. What would be the cost of a 15-mile ride? A B C D A. $18.75 B. $21.50 C. $24.50 D. $27.00 Lesson 4 CYP3

Which expression can be used to find the nth term in the following arithmetic sequence, where n represents a number’s position in the sequence? A. n + 3 B. 3n C. 2n + 1 D. 3n – 1 Lesson 4 Ex4

You need to find an expression to describe any term. Read the Test Item You need to find an expression to describe any term. Solve the Test Item The terms have a common difference of 3 for every increase in position number. So the expression contains 3n. Eliminate choices A and C because they do not contain 3n. Eliminate choice B because 3(1) ≠ 2. The expression in choice D is correct for all the listed terms. So the correct answer is D. Answer: D Lesson 4 Ex4

Let n represent the position of a number in the sequence 7, 11, 15, 19, … Which expression can be used to find any term in the sequence? A. 7n B. 4n – 3 C. 7 – n D. 4n + 3 A B C D Lesson 4 CYP4

End of Lesson 4

Five-Minute Check (over Lesson 10-4) Main Idea Targeted TEKS Example 1: Equations with Variables on Each Side Example 2: Equations with Variables on Each Side Example 3: Real-World Example Lesson 5 Menu

Solve equations with variables on each side. Lesson 5 MI/Vocab

GET THE VARIABLE BY ITSELF!! NOTES The goal of solving EVERY Algebra equation you will ever see for the rest of your life is?????? GET THE VARIABLE BY ITSELF!! To solve equations with variables on each side of the equation: Add or subtract all VARIABLES on ONE side to get rid of them on that side. Add or subtract all the NUMBERS on OTHER side to move them to the side without the variables. Solve it like we’ve been doing all year! HINT: Get rid of the SMALLEST variable term! Lesson 5 TEKS

Equations with Variables on Each Side Solve 7x + 4 = 9x. Check your solution. Write the equation. Subtract 7x from each side. Simplify by combining like terms. Mentally divide each side by 2. To check your solution, replace x with 2 in the original equation. Check Write the equation. ? Replace x with 2.  The sentence is true. Answer: The solution is 2. Lesson 5 Ex1

Solve 3x + 6 = x. Check your solution A. –5 B. –3 C. –1 D. 1 A B C D Lesson 5 CYP1

Equations with Variables on Each Side Solve 3x – 2 = 8x + 13. Write the equation. Subtract 8x from each side. Simplify. Add 2 to each side. Simplify. Mentally divide each side by –5. Answer: The solution is –3. Lesson 5 Ex2

Solve 4x – 3 = 5x + 7. A. –4 B. –7 C. –10 D. –12 A B C D Lesson 5 CYP2

Variable x and 90 – x represent the measures of the angles. GEOMETRY The measure of an angle is 8 degrees more than its complement. If x represents the measure of the angle and 90 – x represents the measure of its complement, what is the measure of the angle? Words 8 less than the measure of an angle equals the measure of its complement. Variable x and 90 – x represent the measures of the angles. Equation x – 8 = 90 – x Lesson 5 Ex3

x – 8 = 90 – x Write the equation. x – 8 + 8 = 90 + 8 – x Add 8 to each side. x = 98 – x x + x = 98 – x + x Add x to each side. 2x = 98 Divide each side by 2. x = 49 Answer: The measure of the angle is 49 degrees. Lesson 5 Ex3

GEOMETRY The measure of an angle is 12 degrees less than its complement. If x represents the measure of the angle and 90 – x represents the measure of its complement, what is the measure of the angle? A. 39 degrees B. 42 degrees C. 47 degrees D. 51 degrees A B C D Lesson 5 CYP3

End of Lesson 5

Five-Minute Check (over Lesson 10-5) Main Idea Targeted TEKS Example 1: Guess and Check Lesson 6 Menu

Guess and check to solve problems. Lesson 6 MI/Vocab

8.14 The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. (C) Select or develop an appropriate problem-solving strategy from a variety of different types, including…systematic guessing and checking…to solve a problem. Lesson 6 TEKS

Guess and Check THEATER 120 tickets were sold for the school play. Adult tickets cost $8 each, and child tickets cost $5 each. The total earned from ticket sales was $840. How many tickets of each type were sold? Explore You know the cost of each type of ticket, the total number of tickets sold, and the total income from ticket sales. Plan Use a systematic guess and check method to find the number of each type of ticket. Lesson 6 Ex1

Check So, 80 adult tickets and 40 child tickets were sold. Guess and Check Solve Find the combination that gives 120 total tickets and $840 in sales. In the list, a represents adult tickets sold, and c represents child tickets sold. Check So, 80 adult tickets and 40 child tickets were sold. Answer: 80 adult and 40 child Lesson 6 Ex1

A. 90 adult tickets, 60 child tickets THEATER 150 tickets were sold for the school play. Adult tickets were sold for $7.50 each, and child tickets were sold for $4 each. The total earned from ticket sales was $915. How many tickets of each type were sold? A. 90 adult tickets, 60 child tickets B. 100 adult tickets, 50 child tickets C. 110 adult tickets, 40 child tickets D. 120 adult tickets, 30 child tickets A B C D Lesson 6 CYP1

End of Lesson 6

Five-Minute Check (over Lesson 10-6) Main Idea Targeted TEKS Example 1: Write Inequalities with < or > Example 2: Write Inequalities with < or > Example 3: Write Inequalities with ≤ or ≥ Example 4: Write Inequalities with ≤ or ≥ Example 5: Determine the Truth of an Inequality Example 6: Determine the Truth of an Inequality Example 7: Graph an Inequality Example 8: Graph an Inequality Lesson 7 Menu

Write and graph inequalities. Lesson 7 MI/Vocab

Look for the following clues: NOTES Translating English to Mathlish Inequalities is similar to converting to equations. Look for the following clues: SOLVING INEQUALITIES Solve inequalities just like you do equations … GET THE VARIABLE BY ITSELF! Lesson 7 TEKS

TO DETERMINE IF INEQUALITIES ARE TRUE TO GRAPH INEQUALITIES NOTES - CONTINUED To check your answer, pick 3 numbers and check them to see if they work in your answer. Pick a number higher Pick a number lower Pick the actual number to see if you need a greater than or equal to sign (or a less than or equal to). TO DETERMINE IF INEQUALITIES ARE TRUE PLUG IN WHAT YOU KNOW AND SEE IF IT’S TRUE!! TO GRAPH INEQUALITIES Graph the point on a number line Figure out if the point should be filled in or not. Use an arrow to show which direction the inequality should go. Lesson 7 TEKS

Write Inequalities with < or > SPORTS Members of the little league team must be under 14 years old. Write an inequality for the sentence. Let a = person’s age. Answer: a < 14 Lesson 7 Ex1

SPORTS Members of the peewee football team must be under 10 years old SPORTS Members of the peewee football team must be under 10 years old. Write an inequality for the sentence. A. a < 10 B. a ≤ 10 C. a > 10 D. a ≥ 10 A B C D Lesson 7 CYP1

Write Inequalities with < or > CONSTRUCTION The ladder must be over 30 feet tall to reach the top of the building. Write an inequality for the sentence. Let b = ladder’s height. Answer: b > 30 Lesson 7 Ex2

CONSTRUCTION The new building must be over 300 feet tall CONSTRUCTION The new building must be over 300 feet tall. Write an inequality for the sentence. A. h < 300 B. h ≤ 300 C. h > 300 D. h ≥ 300 A B C D Lesson 7 CYP2

Write Inequalities with ≤ or ≥ POLITICS The president of the United States must be at least 35. Write an inequality for the sentence. Let a = president’s age. Answer: a ≥ 35 Lesson 7 Ex3

SOFTBALL The home team needs more than 7 points to win SOFTBALL The home team needs more than 7 points to win. Which of the following inequalities describes how many points are needed to win? A. p > 7 B. p ≥ 7 C. p < 7 D. p ≤ 7 A B C D Lesson 7 CYP3

Write Inequalities with ≤ or ≥ CAPACITY A theater can hold a maximum of 300 people. Write an inequality for the sentence. Let p = theater’s capacity. Answer: p ≤ 300 Lesson 7 Ex4

CAPACITY A football stadium can hold a maximum of 10,000 people CAPACITY A football stadium can hold a maximum of 10,000 people. Write an inequality for the sentence. A. p < 10,000 B. p ≤ 10,000 C. p > 10,000 D. p ≥ 10,000 A B C D Lesson 7 CYP4

Determine the Truth of an Inequality For the given value, state whether the inequality is true or false. x – 4 < 6; x = 0 x – 4 < 6 Write the inequality. 0 – 4 < 6 Replace x with 0. ? –4 < 6 Simplify Answer: Since –4 is less than 6, –4 < 6 is true. Lesson 7 Ex5

For the given value, state whether the inequality is true or false. x – 5 < 8; x = 16 A. true B. false A B Lesson 7 CYP5

Determine the Truth of an Inequality For the given value, state whether the inequality is true or false. 3x ≥ 4; x = 1 3x ≥ 4 Write the inequality. 3(1) ≥ 4 Replace x with 1. ? 3 ≥ 4 Simplify. Answer: Since 3 is not greater than or equal to 4, the sentence is false. Lesson 7 Ex6

For the given value, state whether the inequality is true or false. 2x ≥ 9; x = 5 A. true B. false A B Lesson 7 CYP6

Graph n ≤ –1 on a number line. Graph an Inequality Graph n ≤ –1 on a number line. Place a closed circle at –1. Then draw a line and an arrow to the left. Answer: Lesson 7 Ex7

Graph n ≤ –3 on a number line. Answer: Lesson 7 CYP7

Graph n > –1 on a number line. Graph an Inequality Graph n > –1 on a number line. Place an open circle at –1. Then draw a line and an arrow to the right. Answer: Lesson 7 Ex8

Graph n > –3 on a number line. Answer: Lesson 7 CYP8

End of Lesson 7

Five-Minute Checks Image Bank Math Tools Graphing Equations with Two Variables Two-Step Equations CR Menu

Lesson 10-1 (over Chapter 9) Lesson 10-2 (over Lesson 10-1) 5Min Menu

1. Exit this presentation. To use the images that are on the following three slides in your own presentation: 1. Exit this presentation. 2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides. 3. Select an image, copy it, and paste it into your presentation. IB 1

IB 2

IB 3

IB 4

Use the histogram shown in the image. How many people were surveyed? (over Chapter 9) Use the histogram shown in the image. How many people were surveyed? A. 10 B. 12 C. 22 D. 30 A B C D 5Min 1-1

(over Chapter 9) Use the histogram shown in the image. How many people drink more than 3 carbonated beverages per day? A. 2 B. 6 C. 8 D. 12 A B C D 5Min 1-2

(over Chapter 9) Use the histogram shown in the image. What percentage of people drink 2–3 carbonated beverages per day? A. 12 percent B. 20 percent C. 30 percent D. 40 percent A B C D 5Min 1-3

(over Chapter 9) Find the mean, median, and mode for the following set of data. 20, 27, 40, 17, 25, 33, 21 A. about 26.1; 25; none B. about 26.1; 17; none C. about 26.1; 25; 17 D. about 26.1; 17; 40 A B C D 5Min 1-4

(over Chapter 9) Find the range for the following set of data. 20, 27, 40, 17, 25, 33, 21 A. 17 B. 23 C. 25 D. 40 A B C D 5Min 1-5

B. box-and-whisker plot (over Chapter 9) Select an appropriate display for the number of people who prefer skiing to all of the winter sports. A. histogram B. box-and-whisker plot C. circle graph D. line graph A B C D 5Min 1-6

Use the Distributive Property to rewrite the expression 8(y – 3). (over Lesson 10-1) Use the Distributive Property to rewrite the expression 8(y – 3). A. 8y – 3 B. y – 24 C. 8y – 24 D. 8y + 24 A B C D 5Min 2-1

Use the Distributive Property to rewrite the expression –2(11m – n). (over Lesson 10-1) Use the Distributive Property to rewrite the expression –2(11m – n). A. –22m + 2n B. –22m – n C. –11m + n D. –11m – n A B C D 5Min 2-2

Simplify 7k + 9k. A. 15k B. 16k C. 17k D. 18k (over Lesson 10-1) A B C 5Min 2-3

Simplify 14h – 3 – 11h A. 3h – 3 B. –3h + 3 C. –3h – 3 D. 3h + 3 (over Lesson 10-1) Simplify 14h – 3 – 11h A. 3h – 3 B. –3h + 3 C. –3h – 3 D. 3h + 3 A B C D 5Min 2-4

(over Lesson 10-1) Sara has x number of apples, 3 times as many oranges as apples, and 2 peaches. Write an expression in simplest form that represents the total number of fruits. A. 3x – 2 B. 3x + 2 C. 4x – 2 D. 4x + 2 A B C D 5Min 2-5

Which expression represents the perimeter of the triangle? (over Lesson 10-1) Which expression represents the perimeter of the triangle? A. 5x + 1 B. 3x C. 2x – 1 D. 6x A B C D 5Min 2-6

Solve 3n + 2 = 8. Then check your solution. (over Lesson 10-2) Solve 3n + 2 = 8. Then check your solution. A. 2 B. C. D. 4 A B C D 5Min 3-1

Solve 6n – 3 = 21. Then check your solution. (over Lesson 10-2) Solve 6n – 3 = 21. Then check your solution. A. B. 3 C. D. 4 A B C D 5Min 3-2

Solve 2 = 3 – a. Then check your solution. (over Lesson 10-2) Solve 2 = 3 – a. Then check your solution. A. –5 B. –1 C. 1 D. 5 A B C D 5Min 3-3

Solve –5 + 2a – 3a = 11. Then check your solution. (over Lesson 10-2) Solve –5 + 2a – 3a = 11. Then check your solution. A. –16 B. –6 C. 6 D. 16 A B C D 5Min 3-4

(over Lesson 10-2) Jack traveled 5 miles plus 3 times as many miles as Janice. He traveled 23 miles in all. How far did Janice travel? A. 18 miles B. C. D. 6 miles A B C D 5Min 3-5

If 3x – 2 = 16, which choice shows the value of 2x – 3? (over Lesson 10-2) If 3x – 2 = 16, which choice shows the value of 2x – 3? A. B. 6 C. 9 D. 15 A B C D 5Min 3-6

(over Lesson 10-3) Translate the sentence into an equation. Then find the number. The difference of three times a number and 5 is 10. A. 3 – n = 10; 7 B. 3 – n = 10; –7 C. 3n – 5 = 10; –5 D. 3n – 5 = 10; 5 A B C D 5Min 4-1

(over Lesson 10-3) Translate the sentence into an equation. Then find the number. Three more than four times a number equals 27. A. 4n + 3 = 27; 6 B. 3 – 4n = 27; –6 C. D. A B C D 5Min 4-2

(over Lesson 10-3) Translate the sentence into an equation. Then find the number. Nine more than seven times a number is 58. A. B. 7n + 9 = 58; 7 C. D. A B C D 5Min 4-3

(over Lesson 10-3) Translate the sentence into an equation. Then find the number. Four less than the quotient of a number and three equals 14. A. B. C. D. A B C D 5Min 4-4

(over Lesson 10-3) Jared went to a photographer and purchased one 8 x 10 portrait. He also purchased 20 wallet-sized pictures. Jared spent $97 in all, and the 8 x 10 cost $33. How much is each of the wallet-sized photos? A. $2.33 B. $3.20 C. $3.61 D. $6.50 A B C D 5Min 4-5

What is the value of x in the trapezoid? (over Lesson 10-3) What is the value of x in the trapezoid? A. 35 B. 55 C. 70 D. 105 A B C D 5Min 4-6

(over Lesson 10-4) State whether the sequence is arithmetic or not arithmetic. If it is arithmetic, state the common difference. Write the next three terms of the sequence. 32, 38, 44, 50, 56, … A. arithmetic; +6; 62, 68, 74 B. arithmetic; –6; 50, 44, 38 C. not arithmetic; 62, 68, 74 D. not arithmetic; 84, 126, 189 A B C D 5Min 5-1

(over Lesson 10-4) State whether the sequence is arithmetic or not arithmetic. If it is arithmetic, state the common difference. Write the next three of the sequence. 15, 17, 20, 24, 29, … A. arithmetic; +2; 31, 33, 35 B. arithmetic; +3; 32, 35, 38 C. not arithmetic; 31, 33, 35 D. not arithmetic; 35, 42, 50 A B C D 5Min 5-2

(over Lesson 10-4) State whether the sequence is arithmetic or not arithmetic. If it is arithmetic, state the common difference. Write the next three terms of the sequence. 400, 200, 100, 50, 25, … A. arithmetic; –5; 20, 15, 10 B. C. D. not arithmetic; 25, 15, 10 A B C D 5Min 5-3

(over Lesson 10-4) State whether the sequence is arithmetic or not arithmetic. If it is arithmetic, state the common difference. Write the next three terms of the sequence. 2, 4, 12, 24, 72, … A. arithmetic; +48; 120, 168, 216 B. arithmetic +2; 74, 76, 78 C. not arithmetic; 120, 168, 216 D. not arithmetic; 144, 432, 864 A B C D 5Min 5-4

(over Lesson 10-4) What are the first 4 terms of an arithmetic sequence with a common difference of (–6) if the first term is 76? A. 64, 58, 52, 46 B. 76, 70, 64, 58 C. 76, 82, 88, 94 D. 70, 64, 58, 52 A B C D 5Min 5-5

Which sequence is arithmetic? (over Lesson 10-4) Which sequence is arithmetic? A. 4, 8, 16, 32, 64, ... B. 4, 6, 10, 12, 16, ... C. 4, 1, –2, –5, –8, ... D. A B C D 5Min 5-6

Solve 8b – 12 = 5b. Then check your solution. (over Lesson 10-5) Solve 8b – 12 = 5b. Then check your solution. A. –4 B. C. D. 4 A B C D 5Min 6-1

Solve 5c + 24 = c. Then check your solution. (over Lesson 10-5) Solve 5c + 24 = c. Then check your solution. A. –6 B. –4 C. 4 D. 6 A B C D 5Min 6-2

Solve 3x + 2 = 2x – 3. Then check your solution. (over Lesson 10-5) Solve 3x + 2 = 2x – 3. Then check your solution. A. 5 B. 1 C. –1 D. –5 A B C D 5Min 6-3

Solve 4n – 3 = 2n + 7. Then check your solution. (over Lesson 10-5) Solve 4n – 3 = 2n + 7. Then check your solution. A. 5 B. 2 C. –2 D. –5 A B C D 5Min 6-4

(over Lesson 10-5) Todd is trying to decide between two jobs. Job A pays $400 per week plus a 20% commission on everything sold. Job B pays $500 per week plus a 15% commission on everything sold. How much would Todd have to sell each week for both jobs to pay the same? Write an equation and solve. A. 400 + 0.20x = 500 – 0.15x; $285.70 B. 400 + 0.20x = 500 + 0.15x; $2,000 C. 0.20x – 400 = 500 – 0.15x; $2,571.40 D. 0.20x – 400 = 500 + 0.15x; $18,000 A B C D 5Min 6-5

(over Lesson 10-5) Find the value of x so that the pair of polygons shown in the image has the same perimeter. A. 3 B. 4 C. 5 D. 6 A B C D 5Min 6-6

(over Lesson 10-6) The product of two consecutive odd integers is 3,363. What are the integers? Solve using the guess and check strategy. A. 25 and 27 B. 57 and 59 C. 157 and 159 D. 1,681 and 1,682 A B C D 5Min 7-1

(over Lesson 10-6) Jorge decided to buy a souvenir keychain for $2.25, a cup for $2.95, or a pen for $1.75 for each of his 9 friends. If he spent $22.05 on these souvenirs and bought at least one of each type of souvenir, how many of each did he buy? Solve using the guess and check strategy. A. 2 keychains, 4 cups, 3 pens B. 4 keychains, 3 cups, 2 pens C. 3 keychains, 4 cups, 2 pens D. 3 keychains, 2 cups, 4 pens A B C D 5Min 7-2

(over Lesson 10-6) A number squared is 729. Find the number. Solve using the guess and check strategy. A. 27 B. 31 C. 29 D. 25 A B C D 5Min 7-3

A. 5 quarters, 5 dimes, 9 nickels B. 7 quarters, 9 dimes, 3 nickels (over Lesson 10-6) Candace has $2.30 in quarters, dimes, and nickels in her change purse. If she has a total of 19 coins, how many of each coin does she have? Solve using the guess and check strategy. A. 5 quarters, 5 dimes, 9 nickels B. 7 quarters, 9 dimes, 3 nickels C. 2 quarters, 13 dimes, 4 nickels D. 6 quarters, 3 dimes, 10 nickels A B C D 5Min 7-4

(over Lesson 10-6) In the Brown home, there are 30 total legs on people and pets. Each dog and cat has 4 legs, and each family member has 2 legs. The number of pets is the same as the number of family members. How many people are in the Brown family home? Solve using the guess and check strategy. A. 4 people B. 5 people C. 6 people D. 7 people A B C D 5Min 7-5

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