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Solving Multiplication and Division Equations

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EXAMPLE 1 Solving a Multiplication Equation Solve the equation 3x = 45 3 3 x = 15 Check 3x = 45 3 (15) 45 = 45 = 45 Write original equation. Divide each side by 3. Simplify. Write original equation. Substitute 15 for x. Solution checks.

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GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 6a = 54 1. 9 ANSWER 13b = 65 2. 5 ANSWER 8g = 88 3. 11 ANSWER 12n = 108 4. 9 ANSWER

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EXAMPLE 2 Solving a Division Equation Solve the equation x 2 = 0.75. x 2 2 = 2 0.75 x = 1.5 x 2 = 0.75 Write original equation. Multiply each side by 2. Simplify. Check 0.75 = 0.75 Write original equation. Substitute 1.5 for x. Solution checks. x 2 = 0.75. 1.5 2 = 0.75.

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GUIDED PRACTICE for Example 2 Solve the equation. Check your solution. 5. c 2 = 13 26 ANSWER 17 ANSWER 6. d 5 3.4 = 12 ANSWER 7. s 4 = 3 112 ANSWER 10 8. a 11.2 = 105 ANSWER 9. z 7 = 15 30 ANSWER 10. r 6 5 =

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Solving an Equation Using a Reciprocal

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EXAMPLE 3 Solving an Equation Using a Reciprocal Solve the equation 2 3 4 = x 2 3 x ( 3 2 ) ( 4) = ( 3 2 ) 2 3 x 6 = x Write original equation. Multiply each side by, the reciprocal of 3 2 2 3 Simplify.

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GUIDED PRACTICE for Example 3 Solve the equation. Check your solution. 11. 4 5 r = 1 ANSWER 5 4 12. 2 5 2 =t 5 ANSWER 20 ANSWER 13. 1 2 p = 10

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EXAMPLE 4 Standardized Test Practice A blimp travels 300 miles in 7.5 hours. The blimp travels at a constant speed. In Example 4, you’ll write and solve a multiplication equation to find the speed of the blimp. Blimps

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EXAMPLE 4 Standardized Test Practice SOLUTION Use the formula d = rt. d = rt Write formula for distance. Substitute 300 for d and 7.5 for t. Divide each side by 7.5. Simplify. 300 7.5 7.5r 7.5 = 40 = r 300 = r (7.5) ANSWER The speed of the blimp is 40 miles per hour. The correct answer is C

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GUIDED PRACTICE for Example 4 Movie Length A movie is sold as a DVD set that includes 7.5 hours of bonus material. This is 3 times as long as the movie itself. Write and solve an equation to find the length m of the movie. 3m = 7.5; 2.5 h ANSWER

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