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 9
|x - 3| = 5. Find all possible values of x.
If |ax + b| = c, where c > 0, what are the solutions for x?
If |x - 7| = 2, what are the possible values of x?
If |x - a| = 0, what is the value of x?
If |x + b| < c, where c > 0, what is the solution set for x?
If |x| < a, where a > 0, what is the solution set for x?
A number y satisfies the inequality |2y - 1| ≤ 3. What is the range of possible values for y?
A student claims that the solution to |x - 1| = |x + 1| is all real numbers. Is the student correct? Explain your answer.
Which of the following is the solution to |2x + 1| < 5?
(1) -3 < x < 2
(2) -2 < x < 3
(3) -5 < x < 5
(4) -1 < x < 2
Which of the following is the solution to |2x| = 10?
(1) x = 5 only
(2) x = -5 only
(3) x = 5 or x = -5
(4) x = 10 or x = -10
Which of the following is the solution to |x - 2| < 5?
(1) -3 < x < 7
(2) -5 < x < 3
(3) -7 < x < 3
(4) -2 < x < 5
Which of the following is the solution to |x - 2| ≥ 6?
(1) x ≥ 8
(2) x ≤ -4 or x ≥ 8
(3) x ≤ -6 or x ≥ 2
(4) x ≤ 4 or x ≥ 6
Fill in the blank: The solution to |2x - 4| = 0 is x = _______.
Fill in the blank: The solution to |x - 4| = 0 is x = _______.
Fill in the blank: The solution to |x - 6| = 9 is x = _______ or x = _______.
Fill in the blank: The solution to |x + 1| = 6 is x = _______ or x = _______.
True or False: The equation |x| = -4 has no solution.
True or False: The solution to |2x - 1| = -3 is the empty set.
True or False: The solution to |x - 5| > 0 is all real numbers except x = 5.
True or False: The solution to |x + 2| ≤ -1 is the empty set.
