Absolute Value Equation Solver
Absolute Value Equation Solver
An absolute value equation like |ax + b| = c actually hides two separate equations, since the expression inside the bars can be either positive or negative and still produce the same absolute value. Enter the coefficients a, b, and c, and this calculator splits the equation into both cases and solves each one, typically returning two distinct solutions. If c comes out negative, there's no solution at all, since an absolute value can never equal a negative number.
- An absolute value equation |ax + b| = c splits into two cases, since the expression inside the bars can be either positive or negative and still have the same absolute value: ax + b = c, or ax + b = −c.
- This generally produces two distinct solutions, e.g. |2x + 3| = 7 gives x = 2 (from 2x + 3 = 7) and x = −5 (from 2x + 3 = −7).
- If c is negative, there is no solution, since an absolute value can never equal a negative number — and if a = 0, the equation either has infinitely many solutions or none, depending on whether |b| equals c.
How do I solve an absolute value equation |ax + b| = c?
Split it into two linear equations, ax + b = c and ax + b = −c, then solve each one for x separately.
What are the solutions to |2x + 3| = 7?
From 2x + 3 = 7, x = 2. From 2x + 3 = −7, x = −5.
Absolute Value Equation Solver
An absolute value equation like |ax + b| = c actually hides two separate equations, since the expression inside the bars can be either positive or negative and still produce the same absolute value. Enter the coefficients a, b, and c, and this calculator splits the equation into both cases and solves each one, typically returning two distinct solutions. If c comes out negative, there's no solution at all, since an absolute value can never equal a negative number.
- An absolute value equation |ax + b| = c splits into two cases, since the expression inside the bars can be either positive or negative and still have the same absolute value: ax + b = c, or ax + b = −c.
- This generally produces two distinct solutions, e.g. |2x + 3| = 7 gives x = 2 (from 2x + 3 = 7) and x = −5 (from 2x + 3 = −7).
- If c is negative, there is no solution, since an absolute value can never equal a negative number — and if a = 0, the equation either has infinitely many solutions or none, depending on whether |b| equals c.
How do I solve an absolute value equation |ax + b| = c?
Split it into two linear equations, ax + b = c and ax + b = −c, then solve each one for x separately.
What are the solutions to |2x + 3| = 7?
From 2x + 3 = 7, x = 2. From 2x + 3 = −7, x = −5.