Absolute Value Equations and Inequalities
Math ⇒ Algebra
Absolute Value Equations and Inequalities starts at 9 and continues till grade 12.
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See sample questions for grade 12
Describe the difference between the solution sets of |x| < a and |x| > a, where a > 0.
Describe the steps to solve an absolute value equation of the form |ax + b| = c, where c > 0.
Explain why the equation |x + 1| = |x - 1| has two solutions.
Explain why the inequality |x| < -2 has no solution.
If |x - 1| + 2 = 7, what is the value of x?
If |x - 4| = 2x, what are the possible values of x?
If |x + 3| = 2x, find all real solutions for x.
If |x| < 2, what is the interval notation for the solution set?
Which of the following is always true for any real number x?
(1) |x| ≥ 0
(2) |x| ≤ 0
(3) |x| = x
(4) |x| < 0
Which of the following is the correct definition of absolute value?
(1) The distance from x to 0 on the number line
(2) The square of x
(3) The reciprocal of x
(4) The negative of x
Which of the following is the graph of the solution to |x| ≤ 5?
(1) All real numbers
(2) x < -5 or x > 5
(3) -5 ≤ x ≤ 5
(4) x = 5
Which of the following is the solution set for |2x + 1| = 5?
(1) x = 2, x = -3
(2) x = 3, x = -2
(3) x = 2, x = -2
(4) x = 3, x = -3
Fill in the blank: The solution to |2x + 3| > 7 is x < ______ or x > ______.
Fill in the blank: The solution to |x - 7| ≤ 3 is _________.
Fill in the blank: The solution to |x + 4| ≤ 1 is _________.
Fill in the blank: The solution to |x + 5| = 0 is x = _______.
True or False: The equation |x| = 0 has exactly one solution.
True or False: The equation |x| = -4 has no real solution.
True or False: The solution to |x - 2| ≥ 0 is all real numbers.
True or False: The solution to |x + 2| = -1 is x = -3.
