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 12
Describe the steps to solve an absolute value inequality of the form |f(x)| < k, where k > 0.
Explain the general method for solving inequalities of the form |ax + b| < c, where c > 0.
Explain why the inequality |x| < 0 has no solution.
If |x - 1| ≥ 4, what is the solution set?
Solve for x: |3x - 2| ≤ 7.
Solve for x: |5x + 1| > 11.
Solve for x: |x + 4| ≤ 9.
A student claims that the solution to |x - 2| < 0 is x = 2. Is the student correct?
If |x| ≤ 3, which of the following is the correct interval notation for the solution?
(1) (-∞, 3]
(2) [-3, 3]
(3) (-3, 3)
(4) [3, ∞)
Which of the following is the solution set for |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
Which of the following is the solution to |2x - 1| ≤ 3?
(1) -1 ≤ x ≤ 2
(2) -2 ≤ x ≤ 1
(3) -1 ≤ x ≤ 1
(4) 0 ≤ x ≤ 2
Which of the following is the solution to |4 - x| < 6?
(1) -2 < x < 10
(2) -10 < x < 2
(3) -2 < x < 10
(4) 2 < x < 10
Fill in the blank: The inequality |x + 4| > 2 is equivalent to x < ____ or x > ____.
Fill in the blank: The solution to |2x + 3| < 1 is ____ < x < ____.
Fill in the blank: The solution to |3x| ≥ 12 is x ≤ ____ or x ≥ ____.
Fill in the blank: The solution to |x - 5| > 0 is x ≠ ____.
A student claims that the solution to |x - 2| < 0 is x = 2. Is the student correct?
True or False: The inequality |x - 2| < -1 has no solution.
True or False: The inequality |x| < -2 has no solution.
True or False: The solution to |x + 2| ≤ 0 is x = -2.
