One Step Inequality Calculator

The fastest way to use this calculator is to type the inequality exactly as it appears — x + 3 > 7, x - 5 <= 2, 3x >= 12, or -2x > 8. The parser identifies the single operation applied to x and applies the inverse operation to both sides automatically.

After you enter a problem, the Steps tab shows the one move that isolates the variable: subtract, add, divide, or multiply. For addition and subtraction problems, the symbol always stays the same. For multiplication and division problems, the symbol stays the same when the number is positive and flips when the number is negative. The calculator labels the flip explicitly when it happens so the rule is visible rather than just implied by the answer.

If you are new to inequalities, use the Graph tab after the Steps tab. Seeing the result — for example x > 4 — as a shaded ray on a number line makes the solution set concrete. The open or closed circle at the boundary shows whether the boundary value itself is part of the answer.

When the algebra grows beyond one move, step up to the two-step inequality calculator, the multi-step inequality calculator, or the linear inequality calculator for broader first-degree practice.

A one-step inequality is an inequality that requires exactly one operation to isolate the variable. The operation is either addition, subtraction, multiplication, or division. Examples include x + 3 > 7 (subtract 3), x - 5 <= 2 (add 5), 3x >= 12 (divide by 3), and x/4 < 3 (multiply by 4).

One-step inequalities are the first inequality type students encounter in middle school because they are the simplest extension of one-step equations. The algebra is nearly identical — apply the inverse operation to both sides — with one new rule: if the operation involves multiplying or dividing by a negative number, the inequality symbol reverses direction.

That sign-flip rule is the only thing that makes one-step inequalities different from one-step equations. For x + 3 > 7, subtracting 3 gives x > 4, just as it would in an equation. But for -2x > 8, dividing by -2 gives x < -4, not x > -4. The symbol flips because the direction of the inequality reverses when both sides are scaled by a negative factor.

For the graph-first version of the same idea, review inequalities on a number line.

A one-step inequality always ends as a single ray after the inverse operation is applied. The algebra is short, so the graph is often the fastest way to check whether the sign direction stayed correct.

Use an open endpoint for strict symbols (< or >) and a closed endpoint for inclusive symbols (<= or >=). If you want a broader visual refresher on inequalities on a number line, compare the same answer pattern there after solving.

Interval notation is the compact way to write the ray that comes out of a one-step inequality. Parentheses exclude a boundary, brackets include it, and infinity always uses a parenthesis.

Because the algebra is only one move long, interval notation is a good self-check. If the interval direction does not match the graph, revisit whether the final multiplication or division should have flipped the symbol.

The full interval notation guide explains the bracket and parenthesis rules in more detail.