Inequality Solver — ax + b < c (One Variable)
Quick answer: Enter a, b, c and choose the inequality direction to solve ax + b op c for x.
Solve linear inequalities of the form ax + b < c (or >, ≤, ≥) with instant results and step-by-step explanation. Critically, the calculator automatically flips the inequality symbol when dividing by a negative coefficient — the step students most often miss.
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Last reviewed: April 2026Report an error
Solve: ax + b op c
Solution
x < 4
The solution set is x < 4.
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How to Use This Inequality Solver Calculator
- 1Enter a (the coefficient of x).
- 2Enter b (the constant on the left).
- 3Select the inequality operator (<, >, ≤, ≥).
- 4Enter c (the right-hand side).
- 5Read the solution and note if the sign flipped (when a < 0).
Frequently Asked Questions
- Dividing both sides by a negative number reverses the order of the number line. Example: −2x < 6 → x > −3 (sign flips). This is a fundamental rule of inequalities.
- 2x + 3 < 11 → 2x < 8 → x < 4. The solution set is all real numbers less than 4, written (−∞, 4) in interval notation.
- When a = 0 and the inequality is always true (e.g., 5 < 10), every x satisfies it. The solution is all real numbers (−∞, ∞).
- When a = 0 and the inequality is always false (e.g., 5 > 10), no x works.
- This solver handles single inequalities. For compound inequalities like 2 < 3x + 1 < 10, split into two and solve each half separately.
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