Equations with fractions

Solve (x + 4)/2 = (x + 9)/3

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 4 steps.

1. (x + 4)/2 = (x + 9)/3The question.

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

   There are fractions. Multiply both sides by 6 to clear them: 6 is the smallest number that all the bottoms go into.

   3(x + 4) = 2(x + 9)

   Multiplying every term by the same number keeps the balance.

3. Step 2: Expand the brackets on both sides expand

   Expand the brackets first, so you can see all the x terms.

   3x + 12 = 2x + 18

   Multiply the number outside by everything inside.

4. Step 3: Subtract 2x on both sides −2x

   There’s x on both sides. Take away 2x on both sides so x is only on one side. Choosing the smaller x keeps the numbers positive.

   x + 12 = 18

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

   You can add or take away x terms, just like numbers.

5. Step 4: Subtract 12 on both sides −12

   On the left, the x part has + 12 with it. Take 12 away from both sides to get rid of it.

   x = 6

   On the left, the 12 cancels out. x is on its own. x = 6.

   + 12 is undone by − 12.

Answer: x = 6

Check it

Put x = 6 back into the question. If both sides come to the same number, the answer is right.

Left side: (x + 4)/2 → 5

Right side: (x + 9)/3 → 5

✓ Both sides are 5, so x = 6 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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