Unknown on the bottom of a fraction
Solve 9/x + 6 = 10
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 + 6 = 10The question.
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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.
9/x = 4On the left, the 6 cancels out.
Adding 6 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 = 4xNow there’s no x on the left.
Dividing is undone by multiplying.
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Step 3: Divide by 4 on both sides ÷4
4x means 4 × x. Divide both sides by 4 to get x on its own.
9/4 = x9 ÷ 4 doesn’t go exactly, so write it as a fraction: 9/4. As a decimal, that’s 2.25. x is on its own. x = 9/4 (2.25 as a decimal).
Multiplying is undone by dividing.
Answer: x = 9/4 = 2.25
Check it
Put x = 9/4 back into the question. If both sides come to the same number, the answer is right.
Left side: 9/x + 6 → 4 + 6 = 10
Right side: 10 → 10
✓ Both sides are 10, so x = 9/4 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