Equations with fractions

Solve (x − 5)/5 = 8

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 2 steps.

1. (x − 5)/5 = 8The question.

2. Step 1: Multiply by 5 on both sides ×5

   (x − 5)/5 means the bracket is divided by 5. Multiply both sides by 5.

   x − 5 = 40

   Dividing is undone by multiplying.

3. Step 2: Add 5 on both sides +5

   On the left, the x part has − 5 with it. Add 5 to both sides to get rid of it.

   x = 45

   On the left, the 5 cancels out. x is on its own. x = 45.

   − 5 is undone by + 5.

Answer: x = 45

Check it

Put x = 45 back into the question. If both sides come to the same number, the answer is right.

Left side: (x − 5)/5 → 8

Right side: 8 → 8

✓ Both sides are 8, so x = 45 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.

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