Unknown on the bottom of a fraction
Solve 7/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.
- 7/x + 6 = 9The 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.
7/x = 3On 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: 7/x means “7 divided by x”. Multiply both sides by x to get it off the bottom.
7 = 3xNow there’s no x on the left.
Dividing is undone by multiplying.
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Step 3: Divide by 3 on both sides ÷3
3x means 3 × x. Divide both sides by 3 to get x on its own.
7/3 = x7 ÷ 3 doesn’t go exactly, so write it as a fraction: 7/3. x is on its own. x = 7/3.
Multiplying is undone by dividing.
Answer: x = 7/3
Check it
Put x = 7/3 back into the question. If both sides come to the same number, the answer is right.
Left side: 7/x + 6 → 3 + 6 = 9
Right side: 9 → 9
✓ Both sides are 9, so x = 7/3 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