Absolute Value Calculator With Equations
This absolute value calculator does three jobs. Enter one or more numbers to get their absolute values, the distance of each from zero. Enter an equation of the form |ax + b| = c to get both solutions with the steps, or see why there is no solution when c is negative. Or solve an absolute value inequality such as |2x - 3| < 5 or |x + 1| ≥ 4, with the answer in inequality form and interval notation. It explains the split into two cases, so it is useful for algebra homework and checking answers.
Absolute Value Calculator
Find |x| for numbers, or solve |ax + b| = c and absolute value inequalities.
How to use the Absolute Value Calculator
- Choose numbers, equation, or inequality.
- Enter the numbers, or the values of a, b and c.
- For inequalities, pick the sign.
- Read the answer, interval notation and steps.
Absolute value rules
|u| = c means u = c or u = -c. |u| < c means -c < u < c. |u| > c means u < -c or u > c.
Features
- |x| for a list of numbers
- Solves |ax + b| = c
- Solves <, ≤, > and ≥
- Interval notation
- Two-case steps
- No-solution and all-real cases
Frequently asked questions
What is absolute value?
The absolute value of a number is its distance from zero, so it is never negative. |-7| = 7 and |7| = 7.
How do you solve |ax + b| = c?
If c ≥ 0, split into ax + b = c and ax + b = -c, then solve each. |2x - 3| = 5 gives x = 4 or x = -1.
How do you solve |ax + b| < c?
Rewrite as -c < ax + b < c and solve for x. |2x - 3| < 5 gives -1 < x < 4, or (-1, 4).
How do you solve |ax + b| > c?
Split into ax + b > c or ax + b < -c. |x + 1| > 4 gives x < -5 or x > 3.
Can an absolute value equation have no solution?
Yes. |x| = -2 has no solution because an absolute value cannot be negative.