Absolute Value Equation Calculator

Work out absolute value equation instantly with clear inputs, formula shown and shareable results.

About Absolute Value Equation Calculator

Because |u| = c means u = c or u = −c, an absolute value equation splits into two linear equations. There are two solutions when c is positive, one when c is zero and none when c is negative.

Formula

Absolute value equation

|ax + b| = c ⇒ ax + b = ±c ⇒ x = (±c − b)/a

Worked example

With the default values below, Absolute Value Equation Calculator returns Smaller solution of -2.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient a in |ax + b| = c: 2
Constant b: -3
Right-hand side c: 7

Results

Smaller solution: -2.00000000
Larger solution: 5.00000000
Number of solutions: 2
|ax + b| at the first solution: 7.00000000

Step by step

1Values used
2Absolute value equation
3Smaller solution= -2.00000000
4Larger solution= 5.00000000
5Number of solutions= 2
6|ax + b| at the first solution= 7.00000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Solve |2x − 3| = 7.

2x − 3 = 7 gives x = 5, and 2x − 3 = −7 gives x = −2.

Why does a negative right-hand side fail?

Absolute value measures distance from zero, which is never negative.