Absolute Value Inequalities Practice

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

What is ALWAYS the first GOAL in solving an absolute value inequality?

• set up the positive case

• set up the negative case

• isolate the absolute value expression

• multiply or divide by the coefficient of the variable

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5 ... 1 ≤ x ≤ 5

| x + 3 | > 8

• No Solution

• All Real Numbers

• x < -11  or  x > 5

• -5 < x < 11

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5

2t - 3 | - 5 > 16

• No Solution

• All Real Numbers

• t < -2  or  t > 5

• -2 < t < 5

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

• and

• or

Solve for n.

• n ≥ 10 and n ≤ -6

• n > 10 and n < -6

• n ≥ 10 or n ≤ -6

• n > 10 or n < -6

Solve for r.

• r ≥ -38 and r ≤ 32

• r > -38 and r < 32

• r ≥ -38 or r ≤ 32

• r > -38 or r < 32