Solve an equation of the form a x + b = c

The two golden rules

To solve an equation, we transform the equality without breaking it, using two rules:

1. We can add or subtract the same number from both sides.
2. We can multiply or divide both sides by the same (non-zero) number.

As long as we apply the same operation to both sides of the equals sign, the equality remains true.

Step-by-step example

Let’s solve 2x + 3 = 11.

Step 1: We isolate the term with x by subtracting 3 from both sides. 2x + 3 – 3 = 11 – 3 → 2x = 8

Step 2: We divide both sides by 2 (the coefficient of x). 2x / 2 = 8 / 2 -> x = 4

Verification (essential step)

We substitute x = 4 into the original equation: 2 × 4 + 3 = 8 + 3 = 11. This does indeed match the right-hand side: the solution x = 4 is correct.

Common pitfall

Many pupils forget to perform the same operation on both sides, or change a sign by mistake. Example of a common mistake with 3x – 2 = 10:

• Wrong: 3x = 10 – 2 = 8 (we’ve forgotten that –2 becomes +2 when moving to the other side)
• Correct: 3x = 10 + 2 = 12, so x = 4

Rule to remember: when a term moves to the other side, its sign changes (+ becomes -, and vice versa).