Equations with negative numbers

Solve 40 − 2x = 18

The aim is to get x on its own. Whatever we do to one side, we do to the other, so the equation stays balanced. This one takes 3 steps.

1. 40 − 2x = 18The question.

2. Step 1: Add 2x on both sides +2x

   On the left, the x term is −2x, which is negative. Add 2x to both sides, so the x term is positive.

   40 = 18 + 2x

   On the left, the 2x cancels out. Now there’s no x on the left.

   − 2x is undone by + 2x.

3. Step 2: Subtract 18 on both sides −18

   On the right, the x part has + 18 with it. Take 18 away from both sides to get rid of it.

   22 = 2x

   On the right, the 18 cancels out.

   + 18 is undone by − 18.

4. Step 3: Divide by 2 on both sides ÷2

   2x means 2 × x. Divide both sides by 2 to get x on its own.

   11 = x

   x is on its own. x = 11.

   Multiplying is undone by dividing.

Answer: x = 11

Check it

Put x = 11 back into the question. If both sides come to the same number, the answer is right.

Left side: 40 − 2x → 40 − 22 = 18

Right side: 18 → 18

✓ Both sides are 18, so x = 11 is right.

Now try it yourself

Solve this one in Algebra Balance. You choose each step, and it explains what happened, with hints if you get stuck.

Practise this in Algebra Balance

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