Solving Absolute Value Inequalities Interval Notation

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10

• x > 6 or x < -14

• all real numbers

• no solution

What is the first step?

• Get the absolute value alone by dividing both sides by 5

• Drop the absolute value bars and add 7 and 5 together

• Get the absolute value alone by subtracting 5 from both sides

What interval notation does the number line graph represent?

• [∞, -5)

• (∞, -5)

• [-5, ∞)

• (-5, ∞)

Solve.

• no solution

• -6 ≤ r ≥ 8

• 6 > r > -8

• -6 < r < 8

Solve for x:

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve for v:

|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

Solve for d:

3|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32

Which interval notation is represented by the graph?

Solve.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9