Solve the resulting equation

The principle of solving equations

Once the equation has been written, we need to isolate the unknown x, that is, to make it appear on its own on one side of the equals sign. To do this, we apply the same operation to both sides of the equation, so that the equality remains true.

The two basic operations

• If a number is added or subtracted, we perform the inverse operation on both sides.
• If a number is multiplied by x, we divide both sides by that number.

Step-by-step example

Let’s take another look at the equation involving Sarah’s brother: 2 * x + 3 = 27.

Step 1: we subtract 3 from both sides.

2 * x + 3 - 3 = 27 - 3, so 2 * x = 24

Step 2: we divide both sides by 2.

2 * x / 2 = 24 / 2, so x = 12

The brother is therefore 12 years old, and Sarah is x + 3 = 15 years old.

Summary table of inverse operations

Operation in the equation	Operation to reverse it
+ 3	subtract 3
- 7	add 7
* 2	divide by 2
/ 4	multiply by 4

A common pitfall to avoid

A frequent mistake is forgetting to apply the operation to BOTH sides of the equation. If you change just one side, the equation is no longer equivalent and the result becomes incorrect. Also get into the habit of checking your mental calculations at each step: it’s very easy to make a sign error (+ instead of -), which will throw out the entire final result.