Solving Absolute Inequalities

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

| 2w - 1 | < 11

• No Solution

• All Real Numbers

• -5 < w < 6

• -6 < w < 5

2t - 3 | - 5 > 16

• No Solution

• All Real Numbers

• t < -2  or  t > 5

• -2 < t < 5

| 2x + 12 | < 8
Which is the correct first step?

• 2x + 12 < 8 and 2x+12 >-8

• 2x + 12 < 8 or 2x+12 >-8

• 2x + 12 < 8 and 2x+12 <-8

• 2x + 12 < 8 or 2x+12 >-8

What is the first step in solving

|5x + 7| < 22

• Subtract 7 on both sides

• Divide 5 on both sides

• Set up two inequalities

• Set up one inequality

What is the first step in solving |x + 4| - 8 > 2

• Subtract 2 on both sides

• Set up two inequalities

• Divide 8 on both sides

• Add 8 on both sides

Solve the following inequality:

|3x + 6| ≥ 15

• x ≥ 3 or x ≤ −3

• x ≤ 7 and x ≤ −3

• x ≥ 7 and x ≤ −7

• x ≤ −7 or x ≥ 3

Solve.

|4v + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5

• -4.5 ≤ v ≤ -1.4

• -1.5 ≤ v ≤ 4.5

• v ≤ -1.5 or v ≥ 4.5

|x+2| > 3

Please answer in interval notation

• (-Infinity,1)

• (-5,-1)

• (-4,4)

• (-infinity, -5)(1, infinity)

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and"

• separate into two inequalities with an "or"

• divide both sides by -8