Solve an inequality and represent its solution set

By UK GCSE Mathematics · independent study · myAudience

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Solve an inequality and represent its solution set

An inequality often describes a range of inputs rather than a single value. Adding or subtracting the same amount preserves its direction. Multiplying or dividing by a negative number reverses the direction because order on the number line is reversed.

Open circles exclude an endpoint and closed circles include it. For x > −3, use an open circle at −3 and shade to the right. For x ≤ 2, include 2 and shade to the left. The display must match whether equality is permitted.

Check a sample inside the proposed range and, when useful, one outside it. This catches a reversed sign. The check supports the algebra but does not replace the general solving steps.

Worked example: Solve −2x < 6.

Divide both sides by −2.

Reverse < to >.

Represent the range with an open endpoint.

Answer: x > −3.

Check your understanding: Does x = −3 satisfy the original inequality?

Answer: No.

Why: It gives 6 < 6, which is false.