Solving Multiplication and Division Equations
EXAMPLE 1
Solving a Multiplication Equation
Solve the equation
3x = 45
3x = 45
3x = 45
3
3
x = 15
Check
3x = 45
3 (15) 45
=
45 = 45
âś“
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 = 54
1.
9
ANSWER
13b = 65
2.
5
ANSWER
8g = 88
3.
11
ANSWER
12n = 108
4.
9
ANSWER
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.
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 =
Solving an Equation Using a Reciprocal
EXAMPLE 3
Solving an Equation Using a Reciprocal
Solve the equation
2
3
4 =
x
2
3
4 =
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.
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
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
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
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