Equations with fractions

Solve (x + 4)/4 = (x + 7)/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 4 steps.

1. (x + 4)/4 = (x + 7)/5The question.

2. Step 1: Multiply by 20 on both sides ×20

   There are fractions. Multiply both sides by 20 to clear them: 20 is the smallest number that all the bottoms go into.

   5(x + 4) = 4(x + 7)

   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 + 20 = 4x + 28

   Multiply the number outside by everything inside.

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

   There’s x on both sides. Take away 4x on both sides so x is only on one side. Choosing the smaller x keeps the numbers positive.

   x + 20 = 28

   On the right, the 4x 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 20 on both sides −20

   On the left, the x part has + 20 with it. Take 20 away from both sides to get rid of it.

   x = 8

   On the left, the 20 cancels out. x is on its own. x = 8.

   + 20 is undone by − 20.

Answer: x = 8

Check it

Put x = 8 back into the question. If both sides come to the same number, the answer is right.

Left side: (x + 4)/4 → 3

Right side: (x + 7)/5 → 3

✓ Both sides are 3, so x = 8 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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