Page 595 - Basic College Mathematics with Early Integers

572 C HAPTE R 8 I INTRODUCTION TO ALGEBRA

Let’s visualize how we used the addition property of equality to solve the equa-
tion in Example 3. Picture the original equation, x - 2 = 1, as a balanced scale.The
left side of the equation has the same value as the right side.

x 2 1

If the same weight is added to each side of a scale, the scale remains balanced.
Likewise, if the same number is added to each side of an equation, the left side con-
tinues to have the same value as the right side.

x 2 2 1 x 2 2 1 2
or or
x 3

PRACTICE 4 Example 4 Solve: -8 = x + 1
Solve: -1 = z + 9
Solution: To get x alone on one side of the equation, we subtract 1 from both
sides of the equation.
-8 = x + 1
-8 - 1 = x + 1 - 1 Subtract 1 from both sides.
-9 = x + 0 Replace 1 - 1 with 0.
-9 = x Simplify.

Check:
Remember that
-8 = x + 1 we can get the variable alone
-8 -9 + 1 Replace x with -9. on either side of the equa-
-8 -8 True tion. For example, the equa-
tions x = 2 and 2 = x both
The solution is -9. have the solution of 2.
Work Practice 4

PRACTICE 5 Example 5 Solve: y - 1.2 =-3.2 - 6.6
Solve: x - 2.6 =-1.8 - 5.9
Solution: First we simplify the right side of the equation.
y - 1.2 = -3.2 - 6.6
y - 1.2 = -9.8
Next, we get y alone on the left side by adding 1.2 to both sides of the equation.

y - 1.2 + 1.2 =-9.8 + 1.2 Add 1.2 to both sides.
y =-8.6 Simplify.
Check to see that -8.6 is the solution.
Answers Copyright 2012 Pearson Education, Inc.
Work Practice 5
4. -10 5. -5.1

Concept Check Answer Concept Check What number should be added to or subtracted from both
subtract 2.1 from both sides sides of the equation in order to solve the equation -3.75 = y + 2.1?