Equations and Inequalities Chapter 4 Equations and Inequalities

Evaluating and Writing Algebraic Expressions Lesson 4-1 Evaluating and Writing Algebraic Expressions

Vocabulary Variable – a symbol that represents one or more numbers Algebraic expression – a mathematical phrase (number sentence) with at least one variable ***You must THINK your way through this!!

Writing word Phrases Words: $4 per poster times the number of posters Expression: 4 · p Written Algebraically: 4p Words: six goals fewer than g goals Expression: Written Algebraically:

Phrases that mean “ADD” More than Added to Sum Plus Increased by Others? 

Phrases that mean “Subtract” Difference of Minus Subtracted from Less than Decreased by Less Others?

Phrases that mean “Multiply” Of Groups of Product Times Multiply Twice Others? 

Phrases that mean “Divide” Quotient Divide Ratio Into Others? 

Write an algebraic expression for the quantity “three more than half a number”. 2. Write an algebraic expression for the quantity “one-fifth of a number reduced by double the same number”.

3. The number of boxes of cookies sold by Sarah was 43 fewer than the number of boxes of cookies sold by Keiko. The number of boxes of cookies sold by Imelda was 53 more than the number sold by Keiko. Write algebraic expressions for these relations. 4. The first angle of a triangle is 16 degrees less than the second angle. The angle is double the second angle. Write algebraic expressions for these relations.

5. Kentucky has about half the land area of Minnesota 5. Kentucky has about half the land area of Minnesota. The land area of Maine is approximately two-fifths the land area of Minnesota. Write algebraic expressions for these relations. 6. A census of a middle school found that the number of 7th graders was fifty more than the number of eighth graders. The number of sixth graders was three-fourths the number of eighth graders. Write algebraic expressions for these relations.

7. In an archery tournament, the number of points awarded for an arrow in the gold circle (bull’s eye) is six less than triple the points awarded for an arrow in the blue ring. Write algebraic expressions for these relations.

Evaluating Algebraic Expressions Evaluate for p = 2, n = 3, and s = 5 2p + 7 p + (n · s) 2(2) + 7 Substitute (plug it in) 2 + (3)(5) 4 + 7 Solve using PEMDAS 2 + 15 11 17 17 11

Assignment Textbook p. 171 # 12-24/e, 25-30 all, 32-36/e, 40-44 Lesson for Tuesday and Wednesday 1/4 & 1/5

Using Number Sense to Solve Equations Lesson 4-2 Using Number Sense to Solve Equations

Vocabulary Equation – a number sentence with an equal sign Solution of an equation – the value for a variable that makes the equation true Remember – equal means the same on both sides; balanced

Solve using Substitution n – 27 = 38; 11, 51, or 65

Solve using Mental Math

Assignment P. 176 # 10-22/e, 23-25, 33, 38-42 {p. 176 # 10, 14, 18, 22, 23, 25, 33, 38, 39, 40, 41, 42} Work for Thursday 1/6 (still due on Friday)

Solving Equations by Adding or Subtracting Lesson 4-3 Solving Equations by Adding or Subtracting

Vocabulary Inverse operations – operations that undo each other to get the variable alone

Key Concept Addition Property of Equality If you add the same value to each side of an equation, the two sides remain equal: 20/2=10 so 20/2 + 3 = 10 + 3 Subtraction Property of Equality If you subtract the same value to each side of an equation, the two sides remain equal: 12/2=6 so 12/2 -4 = 6 - 4

Examples

Assignment Lesson 4-3 P. 183 # 5-29/all, 40-44/all {p. 183 # 6-28/e, 40-44/all} Tuesday 1-11-11 (Due Friday, No time to make up, it’s on this six week’s grade)

Solving Equations by Multiplying or Dividing Lesson 4-4 Solving Equations by Multiplying or Dividing

Key Concept Since multiplication and division are inverse operations, multiplication undoes division and division undoes multiplication. Example: (4 ∙ 9) ÷ 4 = 9 3/5 ∙ 5 = 3

Examples

Assignment Lesson 4-4 P. 189 # 9-36/all, 53-57/all {p. 189 # 10-36/e, 53-57/all} Wednesday 1-12-11

Exploring Two-Step Problems Lesson 4-5 Exploring Two-Step Problems

Vocabulary A(n) _____________ is a mathematical phrase (number sentence) with at least one variable. Algebraic Expression

Examples Define a variable and write an algebraic expression for the phrase “$10 plus $5 times the number of roses ordered” Define the variable: Let ___= unknown (# roses ordered) Write an algebraic expression:

Examples Define a variable and write an algebraic expression for “a man is two years younger than three times his son’s age” Define the variable: Let ___= unknown ( ) Write an algebraic expression:

Assignment Lesson 4-5 P. 197 # 8-12/all, 14-26/e, 27-28, 38-40/all, 43-48/all {p. 197 # 8, 10, 12, 14, 18, 22, 26, 27, 38, 40, 43-48} Tuesday 1-18-11

Solving Two-Step Problems Lesson 4-6 Solving Two-Step Problems

Examples

Assignment Lesson 4-6 P. 203 # 6-34/e, 43-48 Wednesday 1-19-11

Graphing Inequalities Lesson 4-7 Graphing Inequalities

Examples

Assignment Lesson 4-7 P. 207 # 8-28/e, 37-41 Thursday 1-20-11 (Due Friday 1-28-11)

Solving Inequalities with Addition and Subtraction Lesson 4-8 Solving Inequalities with Addition and Subtraction

Examples

Assignment Lesson 4-8 P. 212 # 8-32/e, 40-46 Monday 1-24-11 (Due Friday 1-28-11)

Solving Inequalities by Multiplying and Dividing Lesson 4-9 Solving Inequalities by Multiplying and Dividing

Examples

Assignment Lesson 4-8 TEST WEDNESDAY 2-2-11 P. 217 # 6-38/e, 50-53 Monday 1-31-11 (Due Wednesday 2-2-11) TEST WEDNESDAY 2-2-11