Solving Multiplication and Division Equations

EXAMPLE 1 Solving a Multiplication Equation

Solve the equation 3x = 45

3x = 45

3x = 453 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.

GUIDED PRACTICE for Example 1

Solve the equation. Check your solution.

6a = 541.

9ANSWER

13b = 652.

5ANSWER

8g = 883.

11ANSWER

12n = 1084.

9ANSWER

EXAMPLE 2 Solving a Division Equation

Solve the equation x2

= 0.75.

x22 = 2 0.75

x = 1.5

x2

= 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.

x2

= 0.75.

1.52

= 0.75.

GUIDED PRACTICE for Example 2

Solve the equation. Check your solution.

5. c 2 = 13

26ANSWER

17ANSWER

6. d5 3.4 =

12ANSWER

7. s 4 = 3

112ANSWER

108. a

11.2 =

105ANSWER

9. z 7 = 15

30ANSWER

10. r6 5 =

Solving an Equation Using a Reciprocal

EXAMPLE 3 Solving an Equation Using a Reciprocal

Solve the equation 23

4 = x

23

4 = x

( 32 ) ( 4) = ( 3

2 ) 23

x

6 = x

Write original equation.

Multiply each side by ,the reciprocal of

322

3

Simplify.

GUIDED PRACTICE for Example 3

Solve the equation. Check your solution.

11. 45

r = 1

ANSWER 54

12. 25

2 = t

5ANSWER

20ANSWER

13. 12

p = 10

EXAMPLE 4 Standardized Test Practice

A blimp travels 300 miles in 7.5 hours. The blimp travelsat a constant speed. In Example 4, you’ll write and solvea multiplication equation to find the speed of the blimp.

Blimps

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.

3007.5

7.5r7.5=

40 = r

300 = r (7.5)

ANSWER The speed of the blimp is 40 miles per hour. The correct answer is C

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 hANSWER