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Solve absolute value equation

Solve |ax + b| = c for x with both branch solutions.

Also known as: solve absolute value equation calculator, absolute value equation calculator, solve absolute value equation, algebra math, algebra solve absolute value equation

Inputs

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Solutions

x = 2.000000, x = -5.000000

|2.0000x + 3.0000| = 7.0000

Steps

CaseEquationSolution
+2.0000x + 3.0000 = 7.0000x = 2.000000
−2.0000x + 3.0000 = −7.0000x = -5.000000
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What this result means

Solve |ax + b| = c for x with both branch solutions. |ax + b| = c → ax + b = c or ax + b = −c (when c ≥ 0).

Assumptions

  • Rule dependency: Universal formula.

Method

|ax + b| = c → ax + b = c or ax + b = −c (when c ≥ 0).

Example

|2x + 3| = 7 → x = 2 or x = −5.

Frequently asked questions

No solution?+

When c < 0, or when a = 0 and |b| ≠ c.