Linear Inequality Solver
Solve a one-variable linear inequality of the form ax + b compared to c and see the solution half-line on a number line.
Comparison
Solution: x < 4
- 1
Subtract b from both sides
c − b = 11 − 3 = 8 - 2
Divide by a
8 ÷ 2 = 4
How does this calculator work?
To solve a·x + b compared to c, isolate x by computing the boundary x0 = (c − b) / a. Keep the comparison direction the same when a is positive, but flip it when a is negative. The solution is the half-line of x values on one side of x0, shown shaded on the number line.
Formula
How this is calculated
Enter the coefficient a and constant b that make the left-hand side a·x + b, choose a comparison operator (<, ≤, >, ≥), and enter the right-hand side value c. The solver first subtracts b from both sides and then divides by a to isolate x, giving the boundary value x0 = (c − b) / a.
The key rule for inequalities is that dividing (or multiplying) both sides by a negative number reverses the direction of the comparison. So when a is negative, the operator is flipped: < becomes >, ≤ becomes ≥, and vice versa. The result is reported as a half-line such as "x > x0" or "x ≤ x0".
The coefficient a must be non-zero; if a = 0 the expression is no longer linear in x and there is no single boundary, so the calculator asks for valid values. The number-line meter shades the solution region (where the inequality holds) versus the excluded region, with the boundary marked at x0. Note the boundary itself is included only for ≤ and ≥.
Frequently asked questions
Dividing or multiplying both sides of an inequality by a negative number reverses the order of the two sides, so the comparison direction must flip. This happens here whenever the coefficient a is negative.
Only for the inclusive operators ≤ and ≥. For strict operators < and >, the boundary x0 itself is excluded and the solution is an open half-line.
Then a·x + b does not depend on x in a linear way and there is no single boundary value, so enter a non-zero coefficient a.
Also known as
TG we-Calculate Editorial Team. (2026). Linear Inequality Solver [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/linear-inequality-solver
TG we-Calculate Editorial Team. "Linear Inequality Solver." TG we-Calculate. 2026. https://we-calculate.com/calculator/linear-inequality-solver.
TG we-Calculate Editorial Team, "Linear Inequality Solver," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/linear-inequality-solver
@misc{wecalculate_linear_inequality_solver, title = {Linear Inequality Solver}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/linear-inequality-solver}}, year = {2026}, note = {TG we-Calculate} }
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