Page 596 - Basic College Mathematics with Early Integers

S E C T I O N 8.2 I SOLVING EQUATIONS: THE ADDITION PROPERTY 573

Example 6 Solve: 5x + 2 - 4x = 7 - 9 PRACTICE 6

Solve: -6y + 1 + 7y = 6 - 11
Solution: First we simplify each side of the equation separately.
5x + 2 - 4x = 7 - 9
5x - 4x + 2 = 7 - 9
3 3
R b
1x + 2 =-2

To get x alone on the left side, we subtract 2 from both sides.
1x + 2 - 2 =-2 - 2
1x =-4 or x =-4

Check to verify that -4 is the solution.
Work Practice 6

7 1
Example 7 Solve: = y - PRACTICE 7
8 2
1 2 4
Solution: We use the addition property of equality to add to both sides. Solve: = x -
2 3 9
7 1
= y -
8 2
7 1 1 1 1
+ = y - + Add to both sides.
8 2 2 2 2
7 4
+ = y Simplify.
8 8
11
= y Simplify.
8
11 11 3
Check to see that is the solution. (Although = 1 , we will leave solutions
8 8 8
as improper fractions.)
Work Practice 7

Example 8 Solve: 3(3x - 5) = 10x PRACTICE 8
Solve: 13x = 413x - 12
Solution: First we multiply on the left side to remove the parentheses.

3(3x-5)=10x
#
#
3 3x - 3 5 = 10x Use the distributive property.
9x - 15 = 10x
Now we subtract 9x from both sides.

9x - 15 - 9x = 10x - 9x Subtract 9x from both sides.
-15 = 1x or x =-15 Simplify.
Work Practice 8

Recall that the addition property of equality allows us to add or subtract the same
number to or from both sides of an equation. Let’s see how adding the same num-
ber to both sides of an equation also allows us to subtract the same number from
both sides.To do so, let’s add 1-c2 to both sides of a = b. Then we have
a + 1-c2 = b + 1-c2 Answers
10
6. -6 7. 8. -4
which is the same as a - c = b - c, and there we have it. 9