Inequality Solver

How it works

1. 1Enter the coefficient a, constant b, an inequality operator, and the right-hand side c to express a·x + b (op) c.
2. 2The solver isolates x by subtracting b from both sides and dividing by a — flipping the operator automatically when a is negative.
3. 3If a = 0 the expression is constant: the result is either all real numbers (always true) or no solution (always false).

Use cases

• Checking homework solutions for one-variable linear inequalities.
• Setting up feasibility constraints in budgeting or scheduling problems.
• Teaching students how dividing by a negative coefficient flips the inequality sign.

Frequently asked questions

Why does the inequality symbol flip?

Multiplying or dividing both sides of an inequality by a negative number reverses the order of the number line, so the direction of the inequality must flip to keep the statement true.

What happens when a = 0?

With a = 0 there is no x term; the inequality reduces to b (op) c, a statement that is either always true (all real numbers) or always false (no solution).

Does this handle strict and non-strict inequalities?

Yes — choose < or > for strict inequalities (open boundary) and ≤ or ≥ for non-strict (closed boundary). The boundary value is the same; only inclusion of the endpoint differs.