Linear inequality solver
Solve ax + b compared to c (<, ≤, > or ≥) for x.
Enter your values and press Calculate. Your inputs stay in the address, so you can switch language or share the link.
Formula
ax + b ⋚ c → x ⋚ (c − b) ÷ a
How it works
Solve it the same way as an equation — but if you multiply or divide both sides by a negative number, the inequality sign must flip direction.
Worked example
The same calculation with the default values:
- Coefficient a 2
- Constant b 3
- Comparison greater than (>)
- Right-hand side c 9
- x = (9 − 3) ÷ 2 = 3
- 2 > 0, sign stays the same: >
Result: Solution: x > 3 · Note: a is positive, so the sign stays the same.
Solves one linear inequality in x. Compound inequalities (two conditions at once) and non-linear inequalities (with x², 1/x, etc.) are outside what this tool handles.
Common mistakes
- Forgetting to flip the inequality sign when dividing or multiplying both sides by a negative number - this is the single most common mistake with inequalities.
- Treating the boundary value as always included or always excluded - whether x can equal the boundary depends on whether you chose < / > (excluded) or ≤ / ≥ (included).
- Solving as if it were an equation and reporting a single number instead of a range.
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