absolute value inequalities

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:
|x + 4| - 8 > 2

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

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

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

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

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

Solve for r.

• r ≥ -38 and r ≤ 32
• r > -38 and r < 32
• r ≥ -38 or r ≤ 32
• r > -38 or r < 32

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

• and
• or

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