11/12 Absolute Value Inequalities

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• 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

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• 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.
-5|x - 4| > -20

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

Solve.
6 - 2|m -3| > -4

• -8 < m < 2
• m < -8 or m > 2
• m < -2 or m > 8
• -2 < m < 8

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

3 | 2t - 3 | - 5 > 16

• No Solution
• All Real Numbers
• t < -2  or  t > 5
• -2 < t < 5

Solve.

• -1 < x < 3

• -1 < x or x < 3

• -1 < x

• x < 3