Algebra 1 Basic

Absolute Value Calculator

Evaluate |x| for any number, or solve equations of the form |ax + b| = c. Includes a number line showing both solutions.

Evaluate |expression|
Solve |ax + b| = c
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Enter values for a, b, and c in |ax + b| = c

| x + | =
|2x + 3| = 7
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Result
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Step-by-Step Solution
Number Line
What is Absolute Value?
  • |x| is the distance from 0 on the number line — always ≥ 0.
  • Distance is never negative, so |−7| = 7 and |7| = 7.
  • |0| = 0 — zero is 0 units from itself.
|x| = x    if x ≥ 0
|x| = −x   if x < 0
Why Two Solutions?

When |expression| = c (with c > 0), the expression equals either c or −c — because both values are the same distance from 0.

Case 1 (positive): ax + b = c
Case 2 (negative): ax + b = −c
Solve each case independently to get x₁ and x₂.

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