Absolute Value Equations and Inequalities

One-Step Absolute Value Inequalities

100

|x|>5

x < -5, x > 5

200

|x+3| > 5

x < -8, x > 2

300

|x+3| > -8

All Real Numbers!

400

|x - 7| < -21

No Solution!

500

|k - 3/2| < 1\2

k < 2, k > 1

Multi-Step Absolute Value Inequalities

100

|k+9| + 8 > 9

k > -8, k < -10

200

|-3 + x| - 2 > 1

x > 6, x < 0

300

|2v-7| + 6 < 5

No Solution!

400

4|-7 + p| > -8

All Real Numbers!

500

9|6b| > 108

x > 2, x < -2

One-Step Absolute Value Equations

100

Solve

|x| = 3

x = 3, x = -3

200

|x| = -4

NO SOLUTION

Absolute value will never evaluate to be a negative number.

300

|x+4| = 8

4, -12

400

|−3r| = 9

3, -3

500

|x/5| = 2

10, -10

Multi-Step Absolute Value Equations

100

|-2x+6| = 6

0, 6

200

|5x| + 5 = 45

8, -8

300

3 |−8x| + 8 = 80

-3, 3

400

3 |3 − 5r| − 3 = 18

-4/5, 2

500

6 |1 − 5x| − 9 = 57

-2, 12/5