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.