Evaluating Absolute Inequalities

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
|x + 3| > - 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve:
|x + 4| + 8 > 2

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

Solve.
|2x - 1| = 7

• x = -3 or x = 4
• x = 4
• x = 4 or x = -4
• no solution

Solve.
|2x - 1| = -7

• x = -3 or x = 4
• all real numbers
• x = 3 or x = -3
• no solution

Solve. 
|2x - 12| + 8  = 8 

• x = 6 or x = -2
• x = 6 or x = -6
• no solution
• x = 6

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

• x < 8 and x > 0
• x > 8 or x < 0
• all real numbers
• no solution