Beginning Algebra, 11th Edition

The addition property of equality says that the same number may be addedto

each side of an equation. In Section 1.5,subtraction was defined as addition of the

opposite. Thus, we can also use the following rule when solving an equation.

88 CHAPTER 2 Linear Equations and Inequalities in One Variable

NOW TRY
EXERCISE 3
Solve .- 15 =x+ 12

NOW TRY

EXERCISE 4

Solve.^23 x- 4 =^53 x

The same number may besubtractedfrom each side of an equation without

changing the solution.

Applying the Addition Property of Equality

Solve

Here, the variable xis on the right side of the equation.

Subtract 22 from each side.

or Rewrite; a number ,

or a number.

CHECK Original equation

Let

✓ True

The check confirms that the solution set is 5 - 296. NOW TRY

- 7 =- 7

- 7 - 29 + 22 x=-29.

- 7 =x+ 22

x=

- 29 =x, x=- 29 =x

- 7 - 22 =x+ 22 - 22

- 7 =x+ 22

- 7 = x+22.

EXAMPLE 3

NOTE In Example 3,what happens if we subtract incorrectly, obtaining

, instead of , as the last line of the solution? A check should indi-

cate an error.

CHECK Original equation from Example 3

Let.

False

The false statement indicates that is nota solution of the equation. If this hap-

pens, rework the problem.

- 15

- 7 = 7

- 7 - 15 + 22 x=- 15

- 7 =x+ 22

x=- 15 x=- 29

- 7 - 22

The left side does

notequal the

right side.

Subtracting a Variable Expression

Solve

Original equation

Subtract from each side.

;

Multiplicative identity property

Check by replacing xwith 17 in the original equation. The solution set is.

NOW TRY

5176

17 =x

8

5 x-

3

5 x=

5

5 x=^1 x

3

5 x-

3

17 = 1 x 5 x= 0

3

5 x

3

5

x+ 17 -

3

5

x=

8

5

x-

3

5

x

3

5

x+ 17 =

8

5

x

3

5 x+^17 =

8

5 x.

EXAMPLE 4

NOW TRY ANSWERS

3. 5 - 276 4. 5 - 46

The variable can be isolated

on eitherside.

From now on we

will skip this step.

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