Solving equations

You buy a snack and a drink for 5 euros in total. The drink costs 2 euros. What did the snack cost? The answer 3 euros probably popped into your head right away. Without noticing, you just solved an equation: x + 2 = 5. Questions like this come up all the time, and one simple idea lets you solve them all the same way.

The equation as a balance scale

An equation is like a balance scale in equilibrium: both sides of the equals sign hold the same amount. In x + 5 = 12, the left side holds an unknown packet x and 5 weights, the right side holds 12 weights. The scale only stays balanced if you do the same thing on both sides: take 5 away on the left, and you must take 5 away on the right too. What remains is x = 7.

Dividing works too

In 3x = 15, three identical packets sit on the left. Divide both sides by 3 and you see what one packet holds: x = 5. Combine both moves and you can crack 2x + 3 = 11 as well. First subtract 3 from both sides, giving 2x = 8. Then divide by 2: x = 4. Always one step at a time, always the same on both sides.

The check: verify it yourself instead of hoping

The best thing about equations: you can check your solution yourself. Just substitute your result into the original equation. For x = 4 in 2x + 3 = 11, you calculate 2 · 4 + 3 = 8 + 3 = 11. It fits! If both sides match, you solved it correctly, no answer key needed.