Question

solve the following using transposition method
$\frac{2x - 1}{2 + x} = \frac{4x - 3}{3 +2x }$
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Answer 1

Answer:

x = 3

Step-by-step explanation:

$\implies$ $\Large{\frac{2x - 1}{2+x}} = \frac{4x-3}{3+2x}$

By cross multiplication,

$\implies$ (3 + 2x) (2x - 1) = (4x - 3) (2 + x)

$\implies$ 2x(3 + 2x) - 1(3 + 2x) = 4x(2 + x) - 3(2 + x)

$\implies$ 6x + 4x² - 3 - 2x = 8x + 4x² - 6 - 3x

$\implies$4x² + 4x - 3 = 4x² + 5x - 6

Transpose everything to LHS

$\implies$ 4x² - 4x² + 4x - 5x - 3 + 6 = 0

$\implies$ - x + 3 = 0

$\implies$ - x = - 3

$\implies$ $\large{\boxed{x\:=3}}$

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