Solving Absolute Value Inequalities

What is the absolute value of -2?

• 0

• 4

• -2

• 2

If the absolute value of x is greater than 2, which of the following is a correct solution?

• x < 2 and x > -2

• x > 2 and x < -2

• x < 2 or x > -2

• x > 2 or x < -2

For the inequality |x| > 7, which of the following is true?

• x < 7 or x > -7

• x > 7 or x < -7

• x < 7 and x > -7

• x > 7 and x < -7

What does the inequality |x| < 3 represent?

• x > 3 or x < -3

• x < 3 or x > -3

• x < 3 and x > -3

• x > 3 and x < -3

In the inequality |x| < k, what is the correct compound inequality?

• x > k or x < -k

• x < k or x > -k

• x > k and x < -k

• x < k and x > -k

For the inequality |2n - 3| > 13, what are the two possible inequalities?

• 2n - 3 > 13 and 2n - 3 < -13

• 2n - 3 > 13 or 2n - 3 < -13

• 2n - 3 < 13 and 2n - 3 > -13

• 2n - 3 < 13 or 2n - 3 > -13

What is the solution for the inequality |2n - 3| > 13?

• n < 8 and n > -5

• n > 8 and n < -5

• n < 8 or n > -5

• n > 8 or n < -5

For the inequality |10k + 3| < 3, what is the correct compound inequality?

• 10k + 3 > 3 or 10k + 3 < -3

• 10k + 3 > 3 and 10k + 3 < -3

• 10k + 3 < 3 or 10k + 3 > -3

• 10k + 3 < 3 and 10k + 3 > -3

What is the solution for the inequality |10k + 3| < 3?

• k > -3/5 and k < 0

• -3/5 > k > 0

• k < -3/5 or k > 0

• -3/5 < k < 0

Why does the inequality |x| ≤ -11 have no solution?

• Absolute value can be zero

• Absolute value can be positive

• Absolute value can be negative

• Absolute value cannot be negative