Solve Absolute Value Inequalities

• no solution
• all real numbers 
• -2 ≤ n ≤ 16
• n ≤ -2 or n ≥ 16

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

Solve.
-5|x - 4| > -20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

What is the correct first step?

• divide by 10

• multiply by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and"

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

| -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

• add 8 to both sides

Solve.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.
|2t + ⅔| < 4

• -5/3 < t < 7/3

• t > 7/3 or t < -5/3

• -7/3 < t < 5/3

• t > 5/3 or t < -7/3

Solve.

3|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32

|d + ⅔| + ¾ < 0

• no solution

• d > -9 and d < ½

• d > -¾ and d < 9

• d < -1/12 and d > -7/12