Beside

Solving Equations: Finding the Missing Number

In one line: Solving an equation means finding the value of the unknown letter (called a variable) that makes both sides equal. You do it by doing the same thing to both sides until the letter is on its own.

Why it works

An equation is a maths sentence with an equals sign, like 3x + 5 = 20, where both sides have the same value. Solving equations is the key skill of algebra. You will use it to work out unknown angles, lengths, prices and speeds, and later in science to rearrange formulas. Once you can keep an equation balanced, you can untangle almost any problem where one number is hidden.

Think of it like: Think of an equation as a balance scale that is perfectly level. The left side and the right side weigh the same. If you take 5 grams off one side, you must take 5 grams off the other side too, or the scale tips. To find the mystery weight x, you keep removing or sharing out equal amounts from both sides until x sits alone on one side, and the other side shows what it weighs. (Where this breaks: A real scale cannot hold negative weights, and you cannot easily picture dividing a pan into thirds, but equations handle negatives, fractions and division with no trouble. The scale only explains why you must do the same thing to both sides, not every move you are allowed to make.)

Worked example

Solve 4x − 7 = 2x + 9.

  1. Get the x terms on one side. Subtract 2x from both sides: 4x − 2x − 7 = 9, so 2x − 7 = 9.
  2. Undo the − 7 using its inverse operation (the opposite operation). Add 7 to both sides: 2x = 16.
  3. 2x means 2 × x, so undo the multiplication. Divide both sides by 2: x = 8.
  4. Check by putting x = 8 back into the original equation: left side 4 × 8 − 7 = 25, right side 2 × 8 + 9 = 25. Both sides match.

Answer: x = 8

Common mistakes

  • Doing an operation to only one side of the equation; fix it by writing the step on both sides every time, like keeping the scale level.
  • Using the wrong inverse, such as subtracting 7 to get rid of − 7; fix it by remembering that adding undoes subtracting and dividing undoes multiplying.
  • Forgetting to multiply every term inside brackets, so 3(x + 4) becomes 3x + 4; fix it by expanding to 3x + 12 before moving anything.
  • Skipping the check at the end; fix it by substituting your answer into the original equation to make sure both sides are equal.

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Solve x + 9 = 15.

Questions parents ask

What year do kids learn solving equations?

Children meet simple missing-number problems in primary school, but formal solving equations with letters usually starts in Year 7 in Australia and the UK, and around Grades 6–7 in the US. By Year 8–9 (Grade 8 in the US) they solve equations with brackets and with the unknown on both sides.

How can I help my child with solving equations at home?

Ask your child to explain each step out loud, saying what they are doing to both sides and why. Encourage them to check every answer by substituting it back into the original equation, and try 'think of a number' puzzles that you can turn into equations together.

Why does my child get the right answer but lose marks?

Many teachers want to see each step written on a new line, with the equals signs lined up, so they can follow the reasoning. Getting into the habit of showing working also helps your child spot their own mistakes on harder equations.

Is it okay to 'move a number to the other side and change its sign'?

It is a shortcut that gives the right result, but it hides the real reason, which is doing the same operation to both sides. Children who learn the balance idea first make fewer sign errors and cope better with harder equations involving fractions and brackets.