A linear inequality like 2x + 1 > 7 is solved almost exactly like an equation: you peel away the operations around x by doing the inverse operation to both sides, until x stands alone. If you can already solve a two-step equation, you can already do most of this.

Subtract 1 from both sides, then divide both sides by 2:

The answer isn't a single number — it's every number bigger than 3, the whole solution set you can picture on a number line.

The one extra rule: flipping the sign

Inequalities behave just like equations under adding and subtracting, and under multiplying or dividing by a positive number. There is exactly one difference:

If you multiply or divide both sides by a negative number, flip the inequality sign.

Take 4 > 2 (true) and divide both sides by -2. Without flipping you'd get -2 > -1, which is false — but -2 < -1 is true. Negating both sides reverses their order, just like reflecting points across 0 on the line (this is the same mirror you meet with negative numbers). So the rule keeps the statement true:

See it solved

Step through the solution of 2x + 1 > 7 one move at a time — each line is the inverse operation applied to both sides — then watch the final step show what happens when the divisor is negative and the sign must flip.

See it explained

Sal Khan works through solving a two-step inequality, including when to reverse the sign.