How this calculation works
If the distance is zero, the two linear equations coincide and produce one root when the slope is nonzero.
THE FORMULA
|ax+b| = c gives ax+b = ±cA worked example
|2x−3| = 5 has roots −1 and 4.
Good to know
A zero slope makes the equation constant.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Solve an absolute value equation by splitting it into two linear equations.
The primary result is labeled “Lower root”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A zero slope makes the equation constant.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
|2x−3| = 5 has roots −1 and 4.
Which rule does this calculator apply?
|ax+b| = c gives ax+b = ±c