At the Red Valley Sports Camp, 15 kids went horseback riding, 14 Properties of Numbers PRE-ALGEBRA LESSON 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis, 23 went hiking, and the rest of the campers stayed in their cabins. If 83 kids were in the camp, how many stayed indoors? 31 2-1

Properties of Numbers Simplify. 1. –18 + (–7) 2. 32 – (–3) PRE-ALGEBRA LESSON 2-1 (For help, go to Lesson 1-5.) Simplify. 1. –18 + (–7) 2. 32 – (–3) 3. (–13) + 6 4. 2 – 48 Check Skills You’ll Need 2-1

Properties of Numbers Solutions PRE-ALGEBRA LESSON 2-1 Solutions 1. –18 + (–7) = –25 2. 32 – (–3) = 32 + 3 = 35 32 – (–3) = 35 3. (–13) + 6 = –7 4. 2 – 48 = 2 + (–48) = –46 2 – 48 = –46 2-1

You can use the Associative Property of Addition to find the total Properties of Numbers PRE-ALGEBRA LESSON 2-1 Carlos spent $42 on his golf game. He then bought a bottle of water for $2 and a chef’s salad for $8. What was the total cost for his golf game and meal? You can use the Associative Property of Addition to find the total cost in two different ways. 42 + (2 + 8) = 42 + 10 = 52 Add 2 and 8 first. (42 + 2) + 8 = 44 + 8 = 52 Add 42 and 2 first. Carlos’s total cost was $52. Quick Check 2-1

Name each property shown. Properties of Numbers PRE-ALGEBRA LESSON 2-1 Name each property shown. a. 17 + x + 3 = 17 + 3 + x Commutative Property of Addition b. (36  2)10 = 36(2  10) Associative Property of Multiplication c.  km = km • 1 Identity Property of Multiplication d.  (103 + 26) + 4 = 103 + (26 + 4) Associative Property of Addition Quick Check 2-1

Use mental math to simplify (48 + 7) + 2. Properties of Numbers PRE-ALGEBRA LESSON 2-1 Use mental math to simplify (48 + 7) + 2. (48 + 7) + 2 = (7 + 48) + 2 Use the Commutative Property of Addition. = 7 + (48 + 2) Use the Associative Property of Addition. = 7 + 50 Add within parentheses. = 57 Add. Quick Check 2-1

= 0.65 + 0.45 + 1.55 Use the Commutative Property of Addition. Properties of Numbers PRE-ALGEBRA LESSON 2-1 Suppose you buy school supplies costing $.45, $.65, and $1.55. Use mental math to find the cost of these supplies. 0.45 + 0.65 + 1.55 = 0.65 + 0.45 + 1.55 Use the Commutative Property of Addition. = 0.65 + (0.45 + 1.55) Use the Associative Property of Addition. = 0.65 + 2.00 Add within parentheses. = 2.65 Add. The cost of the school supplies is $2.65. Quick Check 2-1

Use mental math to simplify (20 • 13) • 5. Properties of Numbers PRE-ALGEBRA LESSON 2-1 Use mental math to simplify (20 • 13) • 5. (20 • 13) • 5 = (13 • 20) • 5 Use the Commutative Property of Multiplication. = 13 • (20 • 5) Use the Associative Property of Multiplication. = 13 • 100 Multiply within parentheses. = 1,300 Multiply. Quick Check 2-1

Name each property shown. 1. d  1 = d Properties of Numbers PRE-ALGEBRA LESSON 2-1 Name each property shown. 1. d  1 = d 2. 3 + (2 + 5) = (3 + 2) + 5 3. f  g = g  f 4. 32 + 45 + 102 = 45 + 32 + 102 Identity Property of Multiplication Associative Property of Addition Commutative Property of Multiplication Commutative Property of Addition 2-1

The Distributive Property PRE-ALGEBRA LESSON 2-2 Evaluate each expression. a. 24 – 6 ÷ 2 • 4 + 36 b. 6 • (3 – 1) + 18 c. 10 + 6 • 5 – 4 ÷ 2 48 30 38 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 (For help, go to Lesson 1-2.) Simplify each expression. 1. 3 • 7 – 9 2. (9 – 5)6 3. 8 + 2 • 6 4. 2(6 – 3) 5. 4 • 5 – 4 • 3 6. 3 • 2 – 1 • 2 Check Skills You’ll Need 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 Solutions 1. 3 • 7 – 9 2. (9 – 5) • 6 21 – 9 4 • 6 12 24 3. 8 + 2 • 6 4. 2 • (6 – 3) 8 + 12 2 • 3 20 6 5. 4 • 5 – 4 • 3 6. 3 • 2 – 1 • 2 20 – 12 6 – 2 8 4 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 Use the Distributive Property to find 15(110) mentally. 15(110) = 15(100 + 10) Write 110 as (100 + 10). = 15 • 100 + 15 • 10 Use the Distributive Property. = 1,500 + 150 Multiply. = 1,650 Add. Quick Check 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 Ms. Thomas gave 5 pencils to each of her 37 students. What is the total number of pencils she gave to the students? (37)5 = (40 – 3)5 Write 37 as (40 – 3). = 40 • 5 – 3 • 5 Use the Distributive Property. = 200 – 15 Multiply. = 185 Subtract. Ms. Thomas gave the students 185 pencils. Quick Check 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 Simplify 11(23) + 11(7). 11(23) + 11(7) = 11(23 + 7) Use the Distributive Property. = 11(30) Add within parentheses. = 330 Multiply. Quick Check 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 Use algebra tiles to multiply 4(3x – 4). Model four groups of 3x – 4. Group like tiles. So 4(3x – 4) = 12x – 16. Quick Check 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 Multiply. a. –9(2 – 8y) –9(2 – 8y) = –9(2) – (–9)(8y) Use the Distributive Property. = –18 – (–72y) Multiply. = –18 + 72y Simplify. b.  (5m + 6)11 (5m + 6)11 = (5m)11 + (6)11 Use the Distributive Property. = 55m + 66 Multiply. Quick Check 2-2

The Distributive Property PRE-ALGEBRA LESSON 2-2 Use the Distributive Property to simplify. 1. 15(203) 2. 7(180) 3. 6(26) – 6(16) 4. (8a – 4)9 5. 2(14 + y) 3,045 1,260 60 72a – 36 28 + 2y 2-2

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 Use numbers to write the following word expression: eight and one-third minus five and two-sevenths. 1 3 2 7 8 – 5 2-3

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 (For help, go to Lesson 2-2.) Simplify each expression. 1. 5(b + 4) 2. –3(2x + 5) 3. 4(–8 – 3q) 4. –6(2b – 7) Check Skills You’ll Need 2-3

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 Solutions 1. 5(b + 4) = 5(b) + 5(4) 2. –3(2x + 5) = –3(2x) + (–3)(5) = 5b + 20 = –6x – 15 3. 4(–8 – 3q) = 4(–8) + 4(–3q) 4. –6(2b – 7) = –6(2b) + (–6)(–7) = –32 – 12q = –12b + 42 2-3

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 Name the coefficients, the like terms, and the constants in 7x + y – 2x – 7. Coefficients: 7, 1, –2 Like terms: 7x, –2x Constant: –7 Quick Check 2-3

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 Simplify 9 + 4f + 3 + 2f. 9 +  4f + 3  + 2f 6f  + 12 Quick Check 2-3

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 Simplify 2b + b – 4. 2b + b – 4 = 2b + 1b – 4 Use the Identity Property of Multiplication. = (2 + 1)b – 4 Use the Distributive Property. = 3b – 4 Simplify. Quick Check 2-3

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 Simplify (7 – 3x)5 + 20x. (7 – 3x)5 + 20x = 35 – 15x + 20x Use the Distributive Property. = 35 + (–15x + 20x) Use the Associative Property of Addition. = 35 + (–15 + 20)x Use the Distributive Property to combine like terms. = 35 + 5x Simplify. Quick Check 2-3

Simplifying Variable Expressions PRE-ALGEBRA LESSON 2-3 Name coefficients, like terms, and constants. 1. 4f – 2f + 3 2. z + 2y – 14 Simplify each expression. 3. 3(a + c – 1) – 2c 4. 4(4v) – 4(v – 9) 4, –2; 4f, –2f; 3 1, 2; none; –14 3a + c – 3 12v + 36 2-3

Variables and Equations PRE-ALGEBRA LESSON 2-4 c 5 Evaluate 10 – for c = 10. 8 2-4

Variables and Equations PRE-ALGEBRA LESSON 2-4 (For help, go to Lesson 1-1.) Write a variable expression for each phrase. 1. the sum of x and 46 2. four less than g 3. t decreased by five 4. the quotient of z and 26 Check Skills You’ll Need 2-4

Variables and Equations PRE-ALGEBRA LESSON 2-4 Solutions 1. the sum of x and 46 2. four less than g x plus 46 g minus 4 x + 46 g – 4 3. t decreased by five 4. the quotient of z and 26 t minus 5 z divided by 26 t – 5 z 26 2-4

Variables and Equations PRE-ALGEBRA LESSON 2-4 State whether each equation is true, false, or an open sentence. Explain. a. 3(b – 8) = 12 open sentence, because there is a variable b. 7 – (–6) = 1 = / false, because 13 1 c. –9 + 5 = – 4 true, because – 4 = – 4 Quick Check 2-4

Variables and Equations PRE-ALGEBRA LESSON 2-4 Write an equation for Six times a number added to the number is the opposite of forty-two. State whether the equation is true, false, or an open sentence. Explain. six times the number Words 6x added to x is the opposite of forty-two –42 the number Equation 6x + = x –42 The equation is an open sentence, because there is a variable. Quick Check 2-4

Variables and Equations PRE-ALGEBRA LESSON 2-4 Is 45 a solution of the equation 120 + x = 75? 120 + x = 75 120 + 45 0 75 Substitute 45 for x. 165 75 = / No, 45 is not a solution of the equation. Quick Check 2-4

Variables and Equations PRE-ALGEBRA LESSON 2-4 A gift pack must hold 20 lb of food. Apples weigh 9 lb and cheese weighs 5 lb. Can the jar of jam that completes the package weigh 7 lb? Equation 5 + = j 20 weight of cheese Words plus = weight of jam. is 20 lb weight of jam 9 weight of apples Let 9 + 5 + j = 20 14 + j = 20 Add. 14 + 7 20 Substitute 7 for the variable. 21 20 = / Quick Check No, the jar of jam cannot weigh 7 lb. 2-4

Variables and Equations PRE-ALGEBRA LESSON 2-4 1. Is b + 3b = 15 true, false, or an open sentence? 2. Write an equation for A number added to seven times the number is the opposite of thirty-two. Is the equation true, false, or an open sentence? 3. Is 25 a solution of the equation 175 – x = 150? 4. Can you stack eight books that are each 3 in. thick inside a box that is 18 in. tall? open sentence 7x + x = –32; open sentence yes no 2-4

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 2 3 Lauralee pitched 12 innings. Maureen pitched 3 fewer innings. How many innings did Maureen pitch? 1 3 8 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 (For help, go to Lesson 2-1.) Simplify each expression. 1. 3 + 4 – 4 2. 7 + 9 – 7 3. 8 – 2 + 2 4. 6 + 2 – 2 Check Skills You’ll Need 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 Solutions 1. 3 + 4 – 4 2. 7 + 9 – 7 = 3 + (4 – 4) = 9 + (7 – 7) = 3 + 0 = 9 + 0 = 3 = 9 3. 8 – 2 + 2 4. 6 + 2 – 2 = 8 + (2 – 2) = 6 + (2 – 2) = 8 + 0 = 6 + 0 = 8 = 6 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 Solve y + 5 = 13. Method 1 Method 2 y + 5 = 13 Subtract 5 y + 5 – 5 = 13 – 5 from each side. y + 5 = 13 – 5 = – 5 y = 8 Simplify. y = 8 Check y + 5 = 13 8 + 5 13 Replace y with 8. 13 = 13 Quick Check 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 Larissa wants to increase the number of books in her collection to 327 books. She has 250 books now. Find the number of books she needs to buy. target number Words plus is 250 number to buy = number to buy. x Let Equation 327 + x 250 = 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 (continued) 327 = 250 + x 327 = x + 250 Use the Commutative Property of Addition. 327 – 250 = x + 250 – 250 Subtract 250 from each side. 77 = x Simplify. Larissa needs to buy 77 more books. Check  Is the answer reasonable? 250 plus the number of books bought should be a total collection of 327. 250 + 77 = 327 Quick Check 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 Solve c – 23 = – 40. c – 23 = – 40 c – 23 + 23 = – 40 + 23 Add 23 to each side. c = –17 Simplify. Quick Check 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 Marcy’s CD player cost $115 less than her DVD player. Her CD player cost $78. How much did her DVD player cost? cost of CD player $115 cost of DVD player Words less than was t = cost of the DVD player. Let 115 Equation 78 – 78 = t – 115 78 + 115 = t – 115 + 115   Add 115 to each side. 193 = t Simplify. Marcy’s DVD player cost $193. Quick Check 2-5

Solving Equations by Adding or Subtracting PRE-ALGEBRA LESSON 2-5 Solve each equation. 1. y + 8 = 12 2. 7 + f – 21 = –20 3. 67 = g – (–36) 4. Ricky rides his bike 12 miles every day. He stops after 7 miles to rest. How much farther does he have to ride? 4 –6 31 5 mi 2-5

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 Divide. Round each quotient to the nearest hundredth. a. b. 0.5952 1.6 10.5126 2.1 0.372, which rounds to 0.37 5.006, which rounds to 5.01 2-6

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 (For help, go to Lesson 1-9.) Simplify each quotient. 1. 2. 3. 4. 18 21 –21 –7 7 –13 Check Skills You’ll Need 2-6

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 Solutions 1. = 1 2. = –1 3. = –1 4. = 1 18 21 –21 –7 7 –13 2-6

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 288 pens are boxed by the dozen. How many boxes are needed? Let Equation 288 = b number of pens Words times number of boxes. is 12 number of boxes • 2-6

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 (continued) 288 = 12b Divide each side by 12. 288 12 12b = 24 = b Simplify. 24 boxes are needed. Check  Is the answer reasonable? Twelve times the number of boxes is the number of pens. Since 12  24 = 288, the answer is reasonable. Quick Check 2-6

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 Solve –2v = –24. –2v = –24 Divide each side by –2. –2v –2 –24 = v = 12 Simplify. Check –2v = –24 –2 • (12) –24 Replace v with 12. –24 = –24 Quick Check 2-6

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 Solve = – 5. x 8 = – 5 x 8 x 8 8 = 8(–5) Multiply each side by 8. x = – 40 Simplify. Quick Check 2-6

Solving Equations by Multiplying or Dividing PRE-ALGEBRA LESSON 2-6 Solve each equation. 1. 8x = –48 2. –2x = 18 3. 108 = 9x 4. = 14 5. –6 = v –3 n 4 –6 –9 12 –42 –24 2-6

Problem Solving Strategy: Guess, Check, Revise PRE-ALGEBRA LESSON 2-7 Find three different odd numbers whose sum is 21. List all possibilities. 1, 3, 17; 1, 5, 15; 1, 7, 13; 1, 9, 11; 3, 5, 13; 3, 7, 11; 5, 7, 9 2-7

Problem Solving Strategy: Guess, Check, Revise PRE-ALGEBRA LESSON 2-7 (For help, go to Lesson 1-5.) Simplify. 1. 158 + 20 2. 158 + 30 3. 158 + 25 4. 158 + 22 5. In Exercises 1–4, which result came closest to 181? Check Skills You’ll Need 2-7

Problem Solving Strategy: Guess, Check, Revise PRE-ALGEBRA LESSON 2-7 Solutions 1. 158 + 20 = 178 2. 158 + 30 = 188 3. 158 + 25 = 183 4. 158 + 22 = 180 5. |181 – 178| = |3| = 3 |181 – 188| = |–7| = 7 |181 – 183| = |–2| = 2 |181 – 180| = |1| = 1 The result of Exercise 4, 180, is the closest to 181. 2-7

Problem Solving Strategy: Guess, Check, Revise PRE-ALGEBRA LESSON 2-7 During the intermission of the play, the Theater Club sold cups of popcorn and soda. The club sold 79 cups of popcorn and 96 sodas for a total of $271. What was the selling price of a cup of popcorn? Of a soda? You can organize conjectures in a table. As a first conjecture, try both with a price of $1. 2-7

Problem Solving Strategy: Guess, Check, Revise PRE-ALGEBRA LESSON 2-7 (continued) Popcorn Soda Price Price Total Price $1 $1 79(1) + 96(1) = 79 + 96 The total is too low. Increase = 175 the price of the popcorn only. $2 $1 79(2) + 96(1) = 158 + 96 The total is too low. = 254 Increase the price of the soda. $2 $2 79(2) + 96(2) = 158 + 192 The total is too high. = 350 Decrease the price of the popcorn. $1 $2 79(1) + 96(2) = 79 + 192 The total is correct. = 271 The popcorn price was $1, and the soda price was $2. Quick Check 2-7

Problem Solving Strategy: Guess, Check, Revise PRE-ALGEBRA LESSON 2-7 Solve using any strategy. 1. A sporting goods store manager ordered twice as many pairs of basketball shoes as tennis shoes. He ordered 96 pairs in all. How many pairs of each did he order? 2. Manuel wrote a 512-word paper over the weekend. He wrote 180 more words on Sunday than he did on Saturday. How many words did he write on Saturday? 32 pairs of tennis shoes; 64 pairs of basketball shoes 166 2-7

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 Order from least to greatest: , 0.25, , – 0.5, 0.3,– 2 1 2 1 6 –2, – 0.5, , 0.25, 0.3, 1 2 6 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 (For help, go to Lesson 1-4.) Graph each set of numbers on a number line. Order the numbers from least to greatest. 1. –3, 7, –9 2. –2, –10, –8 3. 0, 3, –5 4. 3, –6, 10 Check Skills You’ll Need 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 Solutions 1. –9, –3, 7 2. –10, –8, –2 3. –5, 0, 3 4. –6, 3, 10 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 Graph the solutions of each inequality on a number line. a. x > –2   An open dot shows that –2 is not a solution. Shade all the points to the right of –2. b. w –5  A closed dot shows that –5 is a solution. > – Shade all the points to the right of –5. 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 (continued) c. k 4   < – A closed dot shows that 4 is a solution. Shade all the points to the left of 4. d. y < 6 An open dot shows that 6 is not a solution. Shade all the points to the left of 6. Quick Check 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 Write the inequality shown in each graph. a.  x –3   > – b.  x < 3 Quick Check 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 Food can be labeled very low sodium only if it meets the requirement established by the federal government. Use the table to write an inequality for this requirement. Label Definition Sodium-free food Less than 5 mg per serving Very low sodium food At most 35 mg per serving Low-sodium food At most 140 mg per serving 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 (continued) = 35 mg sodium Words number of milligrams of sodium in a serving of very low sodium food. v has at most a serving of very low sodium food Let Equation 35 v < – Quick Check 2-8

Inequalities and Their Graphs PRE-ALGEBRA LESSON 2-8 1. Graph –7 w. 2. Write an inequality for the graph. 3. A child must be at least 50 in. tall to ride on the roller coaster. Write an inequality for this situation. > – x > –30 h 50 > – 2-8

Solving One-Step Inequalities by Adding or Subtracting PRE-ALGEBRA LESSON 2-9 Solve each equation. a. n + 4 = 3 b. 4 – p = 8 n = –1 p = – 4 2-9

Solving One-Step Inequalities by Adding or Subtracting PRE-ALGEBRA LESSON 2-9 (For help, go to Lesson 2-5.) Solve each equation. 1. m + 7 = 5 2. k – 8 = 11 3. 12 + h = 21 4. 6 = n – 23 Check Skills You’ll Need 2-9

Solving One-Step Inequalities by Adding or Subtracting PRE-ALGEBRA LESSON 2-9 Solutions 1. 2. m + 7 – 7 = 5 – 7 k – 8 + 8 = 11 + 8 3. 4. 12 – 12 + h = 21 – 12 m + 7 = 5 m = – 2 12 + h = 21 h = 9 6 = n – 23 29 = n 6 + 23 = n – 23 + 23 k – 8 = 11 k = 19 2-9

Solving One-Step Inequalities by Adding or Subtracting PRE-ALGEBRA LESSON 2-9 Solve each inequality. Graph the solutions. a. 4 + s < 12 4 + s < 12 4 + s – 4 < 12 – 4 Subtract 4 from each side. s < 8 Simplify. b. –16 y – 14 > – –16 y – 14 > – –16 + 14 y – 14 + 14 Add 14 to each side. > – –2 y or y –2 Simplify. > – < Quick Check 2-9

Solving One-Step Inequalities by Adding or Subtracting PRE-ALGEBRA LESSON 2-9 You have 6 GB on your computer. The files you have stored on the hard drive occupy at least 2 GB. How much storage space is left for other files? = storage space available. s Let storage space for our files Words is less than  or equal to plus total space storage space left Inequality 2 6 + < – 2 + s 6 < – 2 – 2 + s 6 – 2 Subtract 2 from each side. < – s 4 Simplify. < – Quick Check No more than 4 GB are left. 2-9

Solving One-Step Inequalities by Adding or Subtracting PRE-ALGEBRA LESSON 2-9 Solve –10 < –13 + q. –10 < –13 + q –10 + 13 < –13 + 13 + q Add 13 to each side. 3 < q Simplify. Quick Check 2-9

Solving One-Step Inequalities by Adding or Subtracting PRE-ALGEBRA LESSON 2-9 Solve each inequality. 1. e + 4 14 2. –22 g – 6 3. A number q plus the opposite of 5 is less than or equal to 0. > – < e 10 < – –16 g > – q 5 < – 2-9

Solving One-Step Inequalities by Multiplying or Dividing PRE-ALGEBRA LESSON 2-10 Solve each equation. a. q ÷ 3 = 6 b. 7r = 21 q = 18 r = 3 2-10

Solving One-Step Inequalities by Multiplying or Dividing PRE-ALGEBRA LESSON 2-10 (For help, go to Lesson 2-6.) Solve each equation. 1. 6x = 24 2. 63 = –7v 3. = 10 4. = 48 x –2 t 6 Check Skills You’ll Need 2-10

Solving One-Step Inequalities by Multiplying or Dividing PRE-ALGEBRA LESSON 2-10 Solutions 1. 2. 3. 4. –2 = –2(10) 6x = 24 x = 4 = 10 x = –20 = 48 t = 288 6 = 48(6) 63 = –7v –9 = v x –2 6x 6 24 63 –7 –7v = t t 6 2-10

Solving One-Step Inequalities by Multiplying or Dividing PRE-ALGEBRA LESSON 2-10 A 1-ton truck has the ability to haul 1 ton, or 2,000 lb. At most, how many television sets can the truck carry if each TV set weighs 225 lb? Let x = number of televisions. Inequality Words number of televisions 225 lb 2,000 lb times is less than or equal to x • 225 2,000 < – 225x 2,000 < – 2-10

Solving One-Step Inequalities by Multiplying or Dividing PRE-ALGEBRA LESSON 2-10 (continued) Divide each side by 225. < – 2,000 225 225x x 8.8 Simplify. Round the answer down to find a whole number of television sets. < – At most, the truck can carry 8 television sets. Check Is the answer reasonable? The total weight of 8 television sets is 8(225) = 1,800 lb, which is less than 2,000 lb but so close that another television set could not be carried. The answer is reasonable. Quick Check 2-10

Solving One-Step Inequalities by Multiplying or Dividing PRE-ALGEBRA LESSON 2-10 Solve –2. z –8 < – –2 z –8 < – Multiply each side by –8 and reverse the inequality symbol. –8(–2) z –8 > – Simplify. z 16 > – Quick Check 2-10

Solving One-Step Inequalities by Multiplying or Dividing PRE-ALGEBRA LESSON 2-10 > – Solve each inequality. 1. 3x –27 2. –5w > 15 3. y 4. 0 5. 4f > –12 –x 5 < 1 4 2 x –9 > – w < –3 y 2 < – x 0 > – f > –3 2-10