4MA1/2HR Jun 2023, Question 17: Rearranging Formulas
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Rearrange y = ∛((6 + 5x)/(x + 4)) to make x the subject, showing the algebraic steps.
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Solution · 4 marks
- 1y = ∛((6 + 5x)/(x + 4))
- 2Cube both sides: y³ = (6 + 5x)/(x + 4)
- 3Multiply both sides by (x + 4): y³(x + 4) = 6 + 5x
- 4Expand the left side: xy³ + 4y³ = 6 + 5x
- 5Gather the x terms on the left: xy³ − 5x = 6 − 4y³
- 6Factorise the left side: x(y³ − 5) = 6 − 4y³
- 7Divide both sides by (y³ − 5): x = (6 − 4y³)/(y³ − 5)
Answer(6 − 4y³)/(y³ − 5)
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