Absolute Value Inequalities

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and

• or

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

Solve:
|x + 4| + 8 > 2

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

Solve.
|2x - 1| = 7

• x = -3 or x = 4

• x = 4

• x = 4 or x = -4

• no solution

Solve.
|2x - 1| = -7

• x = -3 or x = 4

• all real numbers

• x = 3 or x = -3

• no solution

Solve. 
|2x - 12| + 8  = 8 

• x = 6 or x = -2

• x = 6 or x = -6

• no solution

• x = 6

Solve.
-5|x - 4| > 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Solve.
-5|x - 4| < 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

| x + 3 | > 8

• No Solution

• All Real Numbers

• x < -11  or  x > 5

• -5 < x < 11

An absolute value inequality is

• an inequality that contains an absolute value expression

• impossible to solve

• an equation that contains an absolute value expression

• always going to have two solutions