Absolute Value Distance Game
Find two solutions at a given distance from a point on the number line.
Choose Practice or Daily to begin.
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Instructions, device progress and accessibility
Choose Easy, Normal or Hard and select Practice or a daily puzzle based on the UTC date. Enter answers or choose a correction, then select Check answer. Hints and Undo mark a round as assisted. Best scores and progress are stored only in this browser; no account is needed.
Local progress is checked when play begins.
How to play Absolute Value Distance
Choose a difficulty, study the given centre and distance, then enter the smaller and larger possible positions. Select Check answer to see the calculation. A hint explains the distance rule without replacing your answers.
Worked example
Example: |x − 3| = 5 has two solutions. From 3, move 5 units left to −2 or 5 units right to 8. Always check both signs of an absolute-value equation.
Math formulas and key skills
|x − a| = d gives x = a − d or x = a + d for d ≥ 0. The two answers are symmetric around a.
Avoid common mistakes
Do not give just one solution when the distance is positive. Never treat |x| as a sign-changing operation; it describes distance.
Frequently asked questions
Why are there two answers to a distance question?
On a number line, positions to the left and right can be the same distance from the centre.
Can a distance be negative?
No. Absolute value represents a nonnegative distance, so an equation with a negative distance has no real solution.