Solutions of Inequalities Algebra

−6 < 2t − 5 < 3

• −0.5 < t < 1

• 0.5 < t < −1

• −11/2 < t < 2

• 11/2 < t < −2

Look at the Graph. Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

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

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

• -8 < m < 2

• m < -8 or m > 2

• m < -2 or m > 8

• -2 < m < 8

Solve.

• no solution

• -6 ≤ r ≥ 8

• 6 > r > -8

• -6 < r < 8

• r > 11/4 or r < 9/4
• r > 5 or r ≤ 0
• r > 5 or r < 0
• r < -5 or r > 0

Write the inequality in interval notation.

• (-2,5)

• (-∞,-2) or (5,∞)

• [-2,5]

• (-∞,-2] or [5,∞)

Which graph represents the solution to the absolute-value inequality:

I 2x - 11 I < 21

• 
• 
• 
• 

Answer explanation

Remember what sort of graph < means for absolute-value.

Solve.
-5|x - 4| > 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution