Absolute Value Inequalities Calculator
The absolute value inequalities calculator can show you step-by-step how to deal with various inequalities that involve the absolute value of a linear expression - with conversion between inequality and interval notation included!
Solutionx = 5 or x = -2
Case ax + b = +cx = 5
Case ax + b = −cx = -2
Critical points-2 and 5
Check at x = 57should equal 7
The method
|ax + b| = c splits into two cases
Why two cases
|u| = c means u is c units from zero, in either direction — so u = c or u = −c. Solve both.
For inequalities the direction matters: less than traps x between the two critical points (an "and"), while greater than pushes it outside them (an "or"). Getting that backwards is the standard mistake.