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Make f the subject of the formula d = \frac{3(1 - f)}{f - 4} - Edexcel - GCSE Maths - Question 18 - 2020 - Paper 1

Question 18

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Make f the subject of the formula d = \frac{3(1 - f)}{f - 4}

Worked Solution & Example Answer:Make f the subject of the formula d = \frac{3(1 - f)}{f - 4} - Edexcel - GCSE Maths - Question 18 - 2020 - Paper 1

Step 1

Step 1: Clear the Fraction

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Answer

To begin, we can eliminate the fraction by multiplying both sides of the equation by (f - 4):

$d(f - 4) = 3(1 - f)$

Step 2

Step 2: Expand Both Sides

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Answer

Next, we expand both sides of the equation:

$df - 4d = 3 - 3f$

Step 3

Step 3: Rearrange the Terms

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Answer

We then move the terms involving f to one side and the constant terms to the other side:

$df + 3f = 3 + 4d$

Step 4

Step 4: Factor Out f

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Answer

Now, we can factor out f from the left side:

$f(d + 3) = 3 + 4d$

Step 5

Step 5: Solve for f

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Answer

Finally, we isolate f by dividing both sides by (d + 3):

$f = \frac{3 + 4d}{d + 3}$

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