Inequalities, Compound Inequalities and Absolute Value Inequalities

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.
|p + 3| ≥ 10

• -13 ≤ p ≤ 7

• p ≤ -13 or p ≥ 7

• -7 ≤ p ≤ 13

• p ≤ -7 or p ≥ 13

Solve.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3

• c < -5 1/3  or c > 2 2/3

• c < 5 1/3 or c > -2 2/3

• -5 1/3 < c < 2 2/3

x + 1 ≤ -3 or -4x < -8

• x ≤ -4 or x > 2

• x ≤ -4 and x > 2

• x ≤ -2 or x > 2

• x ≤ -2 and x > 2

Solve:

• A

• B

• C

• D

Solve.

• no solution

• -6 ≤ r ≥ 8

• 6 > r > -8

• -6 < r < 8

What is the solution to -1 - 10a < -1 or 10 + 3a < -5 in interval notation?

• [-5, 0)

• (-5, 0)

• (-infinity, -5] or (0, infinity)

• (-infinity, -5) or (0, infinity)

-8<2(x+4) or -3x+4>x-4

• No solutions

• x<-8 or x<2

• x>-8 or x<2

• x<-8 and x<2

Solve.
|4k + 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