Equations with fractions

Solve (x + 5)/2 = (x + 29)/5

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 5 steps.

1. (x + 5)/2 = (x + 29)/5The question.

2. Step 1: Multiply by 10 on both sides ×10

   There are fractions. Multiply both sides by 10 to clear them: 10 is the smallest number that all the bottoms go into.

   5(x + 5) = 2(x + 29)

   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.

   5x + 25 = 2x + 58

   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.

   3x + 25 = 58

   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 25 on both sides −25

   On the left, the x part has + 25 with it. Take 25 away from both sides to get rid of it.

   3x = 33

   On the left, the 25 cancels out.

   + 25 is undone by − 25.

6. Step 5: Divide by 3 on both sides ÷3

   3x means 3 × x. Divide both sides by 3 to get x on its own.

   x = 11

   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: (x + 5)/2 → 8

Right side: (x + 29)/5 → 8

✓ Both sides are 8, 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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