Skill: absolute-value

Absolute Value Practice

An endless supply of never-repeating absolute value problems: evaluate, solve by case analysis, and translate inequalities into intervals and rays — with hints and full solutions.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

How to enter answers

Single answers: an integer like 10 or -4.
Two solutions: separate with a comma, e.g. 8, -2 (any order).
Intervals: type -1 < x < 5.
Two rays: type x < -10 or x > 2.
Impossible: type no solution.

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Evaluate

Absolute value as distance: |−7| + |3| and friends.

|−7| + |3| → 10

Equations

Isolate the bars, then split into two cases. Integer solutions every time.

|x − 3| = 5 → x = 8 or x = −2

Inequalities

Less-than squeezes into an interval; greater-than splits into two rays.

|x − 2| < 3 → −1 < x < 5

3 Watch out for these

The mistakes students make most often on these problems.

1. Writing only one case

Wrong: |x − 3| = 5 gives x = 8 only. Right: x = 8 or x = −2.

2. Splitting before isolating

Wrong: 2|x + 1| = 10 → split immediately. Right: divide by 2 first: |x + 1| = 5.

3. “Or” for less-than

Wrong: |x − 2| < 3 → x < 5 or x > −1. Right: one interval: −1 < x < 5.

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