MyLeoNes™

Linear equations — Mathematics, 11–13 years

Use an unknown number and preserve balance to find what a statement is really saying. Mathematics, 11–13 years.

An equation is a balance

An equation says that two expressions have the same value. The letter is a placeholder for a number we do not know yet, and every legal step must keep both sides equal. Solving means finding the value that makes the statement true.

Why equations help

A word problem can hide its structure inside a story: a fee plus several equal fares, for example. An equation turns that story into a compact balance, so the unknown can be isolated instead of guessed again and again.

Solving 3x + 5 = 20

Start with 3x + 5 = 20. Subtract 5 from both sides: 3x = 15. Divide both sides by 3: x = 5. Check it in the original equation: 3 × 5 + 5 = 20, so the answer fits.

Keep the balance

A common mistake is to subtract 5 from one side of 3x + 5 = 20 but leave the other side unchanged. It feels natural because we are trying to remove the visible 5, yet an equation is a balance: changing one side alone breaks it.

Equations outside school

A phone plan can be written as a fixed monthly charge plus a cost for each extra gigabyte. Equations help compare plans, work out a break-even point or find how many items a budget can buy, as long as the charges really follow that pattern.

Keep exploring

Other languages

Loading MyLeoNes™…