Maths · Algebra and graphs. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
An inequality says that one quantity is bigger or smaller than another. Its solution is a range of values, not a single number. You solve a linear inequality with the same steps as an equation, with one extra rule: if you multiply or divide both sides by a negative number, the inequality sign turns round.
On a number line, an open circle means the end value is not included and a filled circle means it is included.
On a graph, an inequality in x and y describes a region on one side of a line. A broken line means points on the line are not included. A solid line means they are included. Test a point to see which side is wanted.
Students forget to reverse the inequality sign when they divide by a negative number. To avoid this, you can move the x term to the side where it is positive before dividing.
Answer: −2 ≤ x < 3; the integers are −2, −1, 0, 1, 2
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