Equations with fractions

Solve (x + 5)/4 = (x + 14)/7

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)/4 = (x + 14)/7The question.

2. Step 1: Multiply by 28 on both sides ×28

   There are fractions. Multiply both sides by 28 to clear them: 28 is the smallest number that all the bottoms go into.

   7(x + 5) = 4(x + 14)

   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.

   7x + 35 = 4x + 56

   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.

   3x + 35 = 56

   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 35 on both sides −35

   On the left, the x part has + 35 with it. Take 35 away from both sides to get rid of it.

   3x = 21

   On the left, the 35 cancels out.

   + 35 is undone by − 35.

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 = 7

   x is on its own. x = 7.

   Multiplying is undone by dividing.

Answer: x = 7

Check it

Put x = 7 back into the question. If both sides come to the same number, the answer is right.

Left side: (x + 5)/4 → 3

Right side: (x + 14)/7 → 3

✓ Both sides are 3, so x = 7 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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