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🔬 Science ⏱ 3 min read

Understanding Inequality Symbols and Solving Inequalities

Learn what inequality symbols mean, how they differ from equals signs, and the simple steps to solve inequalities in maths.

Age 9–12
KS4 Mathematics KS3 Mathematics Ages 11-14
Reading level: |

What Are Inequality Symbols?

In maths, an inequality is a statement that compares two things and shows that they are not equal. Instead of using the equals sign (=), we use special symbols to show the relationship between numbers.

The main inequality symbols are: < (less than), > (greater than), (less than or equal to), and (greater than or equal to).

Think of it like comparing pocket money. If you have £5 and your friend has £8, you could say your money is < (less than) theirs. If you both have at least £5, you could say you both have ≥ (greater than or equal to) £5.

How Are Inequalities Different from Equations?

An equation uses an equals sign and shows that two things are exactly the same: 3 + 2 = 5. An inequality shows a range of possible answers. For example, x > 5 means x could be 6, 7, 8, 100 — anything bigger than 5, but never 5 itself.

How Do You Solve Inequalities?

Solving inequalities is almost identical to solving equations. You use the same steps: get the unknown letter by itself on one side. For example, if you have x + 3 > 10, subtract 3 from both sides to get x > 7.

There is one important rule to remember: when you multiply or divide both sides by a negative number, you must flip the inequality symbol. So if you have −2x < 8, and you divide by −2, it becomes x > −4.

Think of it like a seesaw. If one side is heavier (>), and you put the same weight on both sides, that relationship stays true. But if you reverse one side (multiply by a negative), the lighter side is now heavier, so you flip your comparison.

Drawing Inequality Solutions

You can show inequality answers on a number line. If x > 5, you draw a circle on 5 (open, because 5 is not included) and shade everything to the right. If x ≥ 5, you fill in the circle (because 5 is included) and shade right.

Inequalities help us describe ranges and limits in real life, from temperature ranges to safety limits on equipment.

Test yourself 🧠

This quiz is calibrated for KS4 Mathematics.