9.3 Equations and Absolute Value

Goal(s): To solve equations involving absolute value

Solve: |x - 3| = 2

• What values can be substituted for “x” to make the equation true?

5 or x 1

Solving Equations with Absolute ValuesTo solve an equation of the form

|A| = bSolve the disjunctionA = b or A = -b

Solve for “x”: |x + 3| = 7

x + 3 = 7

x + 3 = -7

Do not write the absolute value brackets when you set up the two different

equations.

Solve |2x – 4| = 10

x = 7

2 4 10x 2 14x

2 4 10x

2 6x 4 4

3x or

Solve |2x + 5| = 13

x = 4 or x = -9

Solve |3x + 7| = 19

264 or 3

x x

Solve |5x – 3| = -17

No solution. The solution set is

Solving |absolute value| equations:

The absolute value expression must be “by itself” before writing the two different equations.

113 7 |2x+5|7 7

3 | 2 5 | 18x 3 3

| 2 5 | 6x

Solve: |2x – 7| + 5 = 12

| 2 7 | 7x

2 7 7x 2 14x

7x

2 7 7x 2 0x

0x or

Solve |2x + 5| -9 = 12

x = 8 or x = -13

+9 +9|2x + 5| = 21

Solve: 3|2x + 5| -9 = 12

x = 1 or x = -6

+9 +93|2x + 5| = 213 3

2x + 5 = 7 2x + 5 = -7

Assignment:Page 412

(12-32) even