Equations with fractions

Solve (x − 3)/6 = 1

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 − 3)/6 = 1The question.

2. Step 1: Multiply by 6 on both sides ×6

   (x − 3)/6 means the bracket is divided by 6. Multiply both sides by 6.

   x − 3 = 6

   Dividing is undone by multiplying.

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

   On the left, the x part has − 3 with it. Add 3 to both sides to get rid of it.

   x = 9

   On the left, the 3 cancels out. x is on its own. x = 9.

   − 3 is undone by + 3.

Answer: x = 9

Check it

Put x = 9 back into the question. If both sides come to the same number, the answer is right.

Left side: (x − 3)/6 → 1

Right side: 1 → 1

✓ Both sides are 1, so x = 9 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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