Difficulty
Calculator
Interactive practice · 16 questions on solving absolute value equations and inequalities — isolating first, the two-case split, "and" vs "or" forms, no-solution / all-real special cases, and interval notation — with step-by-step solutions.
Press Check answer on each question to see whether you got it right — every check is timestamped and recorded in your Activity log below.
Each attempt is saved under its own name — load, rename, or delete them below. Difficulty / calculator tags are shared across all attempts. Numeric answers accept equivalent forms (e.g. 4/3 or 1.333).
The timer is stopped. Questions are hidden until you resume.
Easy Solve \(|x| = 7\).
Answer: D — \(x = 7\) or \(x = -7\)
Easy Solve \(|x| = 0\).
Answer: A — \(x = 0\) (one solution)
Easy Solve \(|x| = -4\).
Answer: D — no solution
Medium Solve \(|x - 3| = 5\). Select all solutions.
Answer: A, C
Medium Solve \(|2x + 1| = 9\). Select all solutions.
Answer: C, D
Medium Solve \(|x| + 4 = 10\).
Answer: A — \(x = \pm 6\)
Hard Solve \(2|x + 1| - 3 = 7\). Select all solutions.
Answer: A, C
Easy The inequality \(|x| < 5\) is equivalent to:
Answer: D — \(-5 < x < 5\) (interval \((-5,\,5)\))
Medium The inequality \(|x| > 3\) is equivalent to:
Answer: D — \(x < -3\) or \(x > 3\)
Medium Solve \(|x - 1| \le 4\).
Answer: D — \(-3 \le x \le 5\) (interval \([-3,\,5]\))
Hard Solve \(|2x + 3| > 7\).
Answer: C — \(x < -5\) or \(x > 2\)
Medium Solve \(|x| < -2\).
Answer: B — no solution
Medium Solve \(|x| \ge -1\).
Answer: B — all real numbers
Hard Solve \(|3x - 6| \le 9\).
Answer: D — \(-1 \le x \le 5\) (interval \([-1,\,5]\))
Medium Which form of absolute-value inequality produces an "and" (between) solution?
Answer: C — \(|x| < a\) and \(|x| \le a\) (less-than)
Hard Write the solution of \(|x - 2| > 3\) in interval notation.
Answer: A — \((-\infty,\,-1) \cup (5,\,\infty)\)