ClarityHow to use this tool
- Enter coefficient a, constant b, absolute value target c.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
For c ≥ 0, solve ax+b = c and ax+b = −c and remove duplicate roots. If c < 0 no real solution exists because absolute values are nonnegative.
Using coefficient a = 2, constant b = -3, absolute value target c = 5, the result is x = -1 x = 4. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
A positive target can be reached when the inner expression equals either the positive target or its negative. A zero target produces just one root when a is nonzero.
What to keep in mind
Numeric linear expression inside a single absolute value. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.
Common questions
Why can there be two answers?
A positive target can be reached when the inner expression equals either the positive target or its negative. A zero target produces just one root when a is nonzero.
How can I check the result?
For c ≥ 0, solve ax+b = c and ax+b = −c and remove duplicate roots. If c < 0 no real solution exists because absolute values are nonnegative. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.