Absolute Value Inequalities Calculator

Your details

Multiplies the entire absolute value expression. Enter 1 if there is no coefficient.
Multiplies x inside the absolute value bars.
The constant term added to bx inside the absolute value bars. Use negative values for subtraction.
A constant added outside the absolute value expression.
The value on the right side of the inequality.
Choose the inequality sign between the left-hand side and the right-hand side.
Solution setBounded interval
-2 < x < 8

The solution expressed as a compound inequality.

Interval notation(-2, 8)
Solution typeAND (intersection) - bounded interval
Simplified right-hand side5
Lower bound x-2
Upper bound x8
Lower bound-2
Upper bound8
Simplified RHS (k)5

Solution: -2 < x < 8

  • The solution is a bounded interval of width 10, centered at x = 3.
  • Any x between -2 and 8 (inclusive based on your sign) makes |x - 3| < 5 true.
  • For "less than" absolute value inequalities the solution is always a bounded AND interval, meaning x is squeezed between two values.
  • In interval notation: (-2, 8).

Next stepTo verify your answer, pick a test value from inside the solution region and confirm it satisfies the original inequality, then pick one outside and confirm it does not.

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