Inequalities with Absolute Value
Math ⇒ Algebra
Inequalities with Absolute Value starts at 8 and continues till grade 12.
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See sample questions for grade 11
Describe the steps to solve an inequality of the form |ax + b| < c, where c > 0.
Explain how to solve an inequality of the form |x - a| ≤ b, where b ≥ 0.
Explain the difference between the solution sets of |x| < a and |x| > a, where a > 0.
Explain why the inequality |x + 1| < 0 has no solution.
If |x + 4| < 0, what is the solution set?
If |x| ≤ 0, what is the value of x?
Solve for x: |3x - 2| ≤ 7.
Solve for x: |4x - 8| ≤ 0.
If |x - 5| > 0, which of the following is the solution set?
(1) x = 5
(2) x ≠ 5
(3) x > 5
(4) x < 5
If |x| < 1, which of the following is true?
(1) x > 1
(2) -1 < x < 1
(3) x < -1
(4) x = 1 or x = -1
Which of the following is the correct solution to |x| ≥ 6?
(1) x > 6
(2) x < 6
(3) x ≤ -6 or x ≥ 6
(4) -6 < x < 6
Which of the following is the solution to |2x + 1| ≥ 7?
(1) x ≤ -4 or x ≥ 3
(2) x ≤ -3 or x ≥ 4
(3) x ≤ -5 or x ≥ 2
(4) x ≤ -2 or x ≥ 5
Fill in the blank: The inequality |x + 2| > 6 is equivalent to x < _____ or x > _____.
Fill in the blank: The solution to |2x - 5| < 9 is _____ < x < _____.
Fill in the blank: The solution to |3x| > 9 is x < _____ or x > _____.
Fill in the blank: The solution to |5 - x| ≥ 2 is x ≤ _____ or x ≥ _____.
True or False: The inequality |x| ≤ -2 has no solution.
True or False: The solution to |2x + 1| ≤ 0 is x = -0.5.
True or False: The solution to |x - 2| ≤ 0 is x = 2.
True or False: The solution to |x| < 4 is all real numbers x such that -4 < x < 4.
