Unknown on the bottom of a fraction
Solve 9/x + 9 = 14
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.
- 9/x + 9 = 14The question.
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Step 1: Subtract 9 on both sides −9
On the left, + 9 is stuck to the fraction. Take it away on both sides first, so the fraction is on its own.
9/x = 5On the left, the 9 cancels out.
Adding 9 is undone by taking it away.
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Step 2: Multiply by x on both sides ×x
x is on the bottom of a fraction: 9/x means “9 divided by x”. Multiply both sides by x to get it off the bottom.
9 = 5xNow there’s no x on the left.
Dividing is undone by multiplying.
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Step 3: Divide by 5 on both sides ÷5
5x means 5 × x. Divide both sides by 5 to get x on its own.
9/5 = x9 ÷ 5 doesn’t go exactly, so write it as a fraction: 9/5. As a decimal, that’s 1.8. x is on its own. x = 9/5 (1.8 as a decimal).
Multiplying is undone by dividing.
Answer: x = 9/5 = 1.8
Check it
Put x = 9/5 back into the question. If both sides come to the same number, the answer is right.
Left side: 9/x + 9 → 5 + 9 = 14
Right side: 14 → 14
✓ Both sides are 14, so x = 9/5 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