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AQA GCSE · Question 17 · Algebra
Rearrange y = (3x + 7) / x to make x the subject.
Rearrange y = (3x + 7) / x to make x the subject.
How to approach this question
1. The first step is to get rid of the fraction. Multiply both sides of the equation by the denominator, `x`.
2. Your goal is to get all the terms with `x` in them on one side of the equation and everything else on the other side.
3. Once you have all the `x` terms on one side (e.g., `xy - 3x`), you need to factorise `x` out of the expression.
4. Finally, divide by the bracket to leave `x` as the subject.
Full Answer
Step 1: Multiply both sides by x to eliminate the fraction.
y * x = 3x + 7
xy = 3x + 7
Step 2: Collect all terms containing x on one side of the equation. Subtract 3x from both sides.
xy - 3x = 7
Step 3: Factorise the left side by taking out the common factor, x.
x(y - 3) = 7
Step 4: Isolate x by dividing both sides by the bracket (y - 3).
x = 7 / (y - 3)
Answer: x = 7 / (y - 3)
We want to rearrange the formula y = (3x + 7) / x to make x the subject. This means we need to get x on its own on one side of the equation.
1. **Eliminate the fraction:** Multiply both sides by x.
y * x = (3x + 7)/x * x
xy = 3x + 7
2. **Group x terms:** Get all terms containing x onto the same side. Subtract 3x from both sides.
xy - 3x = 7
3. **Factorise:** Since x appears in two terms, we can't simply combine them. We need to take x out as a common factor.
x(y - 3) = 7
4. **Isolate x:** Now x is only written once. To get it by itself, divide both sides by the expression in the bracket, (y - 3).
x = 7 / (y - 3)
Common mistakes
✗ Trying to divide by x at the start, which complicates the equation.
✗ Incorrectly rearranging terms, especially with signs (e.g., xy = 7 - 3x).
✗ A common error is to "cancel" the x's in (3x+7)/x to get 3+7. This is incorrect.
✗ Forgetting to factorise and getting stuck at `xy - 3x = 7`.
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