Unknown on the bottom of a fraction

Solve 3/x + 6 = 9

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 3 steps.

1. 3/x + 6 = 9The question.

2. Step 1: Subtract 6 on both sides −6

   On the left, + 6 is stuck to the fraction. Take it away on both sides first, so the fraction is on its own.

   3/x = 3

   On the left, the 6 cancels out.

   Adding 6 is undone by taking it away.

3. Step 2: Multiply by x on both sides ×x

   x is on the bottom of a fraction: 3/x means “3 divided by x”. Multiply both sides by x to get it off the bottom.

   3 = 3x

   Now there’s no x on the left.

   Dividing is undone by multiplying.

4. Step 3: Divide by 3 on both sides ÷3

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

   1 = x

   x is on its own. x = 1.

   Multiplying is undone by dividing.

Answer: x = 1

Check it

Put x = 1 back into the question. If both sides come to the same number, the answer is right.

Left side: 3/x + 6 → 3 + 6 = 9

Right side: 9 → 9

✓ Both sides are 9, so x = 1 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

More like this

• 3/x + 7 = 13
• 7/x + 1 = 7
• 11/x + 7 = 10
• 2/x + 1 = 7
• 6/x + 2 = 3
• 5/x + 4 = 9
• 9/x + 1 = 4
• 4/x + 9 = 11