1. Combine like terms
Subtract cx from both sides, then subtract b from both sides. These addition and subtraction steps do not change the inequality direction.
x < 5
Interval notation(−∞, 5)
Inequality Solver with Interval Notation and Number Line
Get the isolated inequality, exact boundary, interval and set-builder notation, sign-reversal steps, and an accessible number-line graph.
Enter a linear inequality
Solution and number line
Solved inequality
Set-builder notation{x ∈ ℝ | x < 5}
Boundary5 (excluded)
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Step-by-step solution
The algebra steps will appear here.
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How to solve a linear inequality
Collect the variable terms on one side and constants on the other. For ax + b ? cx + d:
(a − c)x ? d − b
2. Divide carefully
Divide by a−c. If that value is negative, reverse < with >, or ≤ with ≥.
3. Choose the endpoint
Strict < and > use an open circle and parenthesis. Inclusive ≤ and ≥ use a closed circle and bracket at a finite endpoint.
4. Check cancellation
If a−c=0, the variable cancels. A true constant comparison gives all real numbers; a false one gives the empty set.
Worked inequality examples
Strict upper bound
3x+7<22 becomes 3x<15, then x<5. Interval: (−∞,5).
Negative coefficient
−2x+5≥13 becomes −2x≥8. Dividing by −2 reverses the sign: x≤−4, or (−∞,−4].
Variables on both sides
5x−1>2x+8 becomes 3x>9, so x>3. Interval: (3,∞).
Variables cancel
2x+3<2x+8 reduces to 3<8, which is always true. The solution is all real numbers: (−∞,∞).
Calculation method, privacy, and limits
Integers, fractions, and finite decimals are converted to reduced fractions and processed with BigInt arithmetic. Boundaries and comparisons are exact; decimal approximations are shown only when they add useful context.
Each numeric part is limited to 30 digits to keep browser calculations responsive. Scientific notation and repeating-decimal notation are not accepted; enter an exact fraction instead. All solving happens in your browser, and the calculator does not transmit or store inequality inputs. Last reviewed: 4 August 2026.
Inequality solver FAQs
When do I reverse an inequality sign?
Reverse it when you multiply or divide both sides by a negative number. For example, dividing −2x>6 by −2 gives x<−3.
How do I write an inequality in interval notation?
Use parentheses for excluded endpoints and brackets for included finite endpoints. Infinity always takes a parenthesis, so x≥4 is [4,∞).
What do open and closed circles mean?
An open circle excludes the boundary for < or >. A closed circle includes it for ≤ or ≥.
Can the answer be all real numbers or no solution?
Yes. When the x terms cancel, test the remaining constants. A true comparison applies to every real x; a false comparison applies to none.
Can I enter fractions and decimals?
Yes. Use integers, finite decimals, or fractions such as -3/4. Exact fractions are reduced automatically.
Is this inequality solver private?
Yes. It solves locally in your browser and does not send or store the values you enter.