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Make x the subject of the formula y frac 3x - 9... - JAMB Mathematics 2023 Question

 

Make x the subject of the formula:y = \(\frac {3x - 9c}{4x + 5d}\)

A

x = \(\frac {(-9c - 5dy)}{4y - 3}\)

B

x = \(\frac {-9c + 5dy}{4y - 3}\)

C

x = \(\frac {(-9c + 5dy)}{4y - 3}\)

D

x = \(\frac {-9c - 5dy}{4y - 3}\)

correct option: a

To solve for \(x\), let's start with the given formula:

\[ y = \frac{3x - 9c}{4x + 5d} \]

Cross-multiplying to eliminate the fraction:

\[ y(4x + 5d) = 3x - 9c \]

Expanding and simplifying:

\[ 4xy + 5dy = 3x - 9c \]

Bringing all \(x\)-related terms to one side:

\[ 4xy - 3x = -9c - 5dy \]

Factoring out \(x\):

\[ x(4y - 3) = -9c - 5dy \]

Now, solving for \(x\):

\[ x = \frac{-9c - 5dy}{4y - 3} \]

This matches Option A:

\[ x = \frac{-9c - 5dy}{4y - 3} \]

 

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