Page 602 - Basic College Mathematics with Early Integers

S E C T I O N 8.3 I SOLVING EQUATIONS: THE MULTIPLICATION PROPERTY 579

Check: To check, we replace a with 15 in the original equation.
3
a = 9 Original equation
5
3
# 15 9 Replace a with 15.
5
3
3 15
# 9 Multiply.
5 1
1
9 9 True

3
Since 9 = 9 is true, 15 is the solution of a = 9.
5
Work Practice 4

1 1
Example 5 Solve: - x = PRACTICE 5
4 8
7 2
4 1 Solve: - x =
Solution: We multiply both sides of the equation by - , the reciprocal of - . 10 5
1 4
1 1
- x =
4 8
4 1 4 1 4
- # - x = - # Multiply both sides by - .
1 4 1 8 1
1
#
4 1
#
1 x =- Multiply.
1 # 8
2
1
x =- Simplify.
2
1
Check to see that - is the solution.
2
Work Practice 5

Concept Check Which operation is appropriate for solving each of the fol-
lowing equations, addition or division?
a. 6 =-4x
b. 6 = x - 4

We often need to simplify one or both sides of an equation before applying the
properties of equality to get the variable alone.

Example 6 Solve: 3y - 7y = 12 PRACTICE 6
Solve: 2m - 4m = 10
Solution: First we combine like terms.
3y - 7y = 12
-4y = 12 Combine like terms.
Answers
-4y 12
= Divide both sides by -4. 4
-4 -4 5. - 7 6. -5
y =-3 Simplify
Concept Check Answers
Continued on next page a. division b. addition