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Absolute Value Inequality Solver

Solve absolute-value inequalities such as |x+3| < 5 or |x−2| > 3 and get the solution as an interval, with AND/OR reasoning explained step by step.

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Absolute Value Inequality Solver is free to use as often as you like, directly from this page. Its place is under Algebra & equations; Absolute Value Equation Solver and Inequality Solver answer the questions closest to this one.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Absolute Value Inequality Solver do?

Solve absolute-value inequalities such as |x+3| < 5 or |x−2| > 3 and get the solution as an interval, with AND/OR reasoning explained step by step.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Absolute Value Inequality Solver different from Absolute Value Equation Solver?

They sit next to each other but answer different questions: Absolute Value Equation Solver is the one to open when you need it to solve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Inequality Solver is the closest one after this: Solve linear, quadratic and rational inequalities such as x^2-5x+6>0 or (x+2)/(x-1)>0 with a full sign chart and the solution set in interval notation.

What else is worth having open alongside it?

Cubic Equation Solver and Exponential Equation Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerRelative Risk and Absolute Risk Are Not the Same StoryA headline saying 50% higher risk can describe a change of two-tenths of a percentage point. Both numbers come from the same 2x2 table, and computing both takes one line each — here is how, with a worked example, number needed to treat, and where the odds ratio stops approximating relative risk.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.