Equations with fractions

Solve (x + 6)/3 = (x + 11)/4

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 + 6)/3 = (x + 11)/4The question.

2. Step 1: Multiply by 12 on both sides ×12

   There are fractions. Multiply both sides by 12 to clear them: 12 is the smallest number that all the bottoms go into.

   4(x + 6) = 3(x + 11)

   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.

   4x + 24 = 3x + 33

   Multiply the number outside by everything inside.

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

   There’s x on both sides. Take away 3x on both sides so x is only on one side. Choosing the smaller x keeps the numbers positive.

   x + 24 = 33

   On the right, the 3x 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 24 on both sides −24

   On the left, the x part has + 24 with it. Take 24 away from both sides to get rid of it.

   x = 9

   On the left, the 24 cancels out. x is on its own. x = 9.

   + 24 is undone by − 24.

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 + 6)/3 → 5

Right side: (x + 11)/4 → 5

✓ Both sides are 5, 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.

Practise this in Algebra Balance

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