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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