Solving Absolute Inequalities

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5

| x + 3 | > 8

• No Solution

• All Real Numbers

• x < -11  or  x > 5

• -5 < x < 11

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

• and

• or

Solve for v.

• v ≥ -6 and v ≤ -4

• v > -6 and v < -4

• v ≥ -6 or v ≤ -4

• v > -6 or v < -4

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

• no solution
• -6 < x < 26
• x < -6 or x > 26
• all real numbers

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

What is the correct first step?

• divide both sides by 10

• multiply both sides by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and" or a between statement

Solve for r.

• r ≥ -38 and r ≤ 32

• r > -38 and r < 32

• r ≥ -38 or r ≤ 32

• r > -38 or r < 32

| x | ≤ 3.5

• No Solution

• All Real Numbers

• -3.5 ≤ x ≤ 3.5

• x ≤ -3.5  or  x ≥ 3.5