Question

$\frac{4x + 9}{3x+11} = \frac{4x + 3}{3x + 2}$
Find the value of x.

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Answer 1

Answer:

Given Question :

$\sf \: \frac{4x + 9}{3x + 11} = \frac{4x + 3}{3x + 2}$

To Find :

The value of x =?

Solution :

By using cross - multiplication method,

$\rightarrow \: \sf \: (4x + 9)(3x + 2) = (4x + 3)(3x + 11) \\ \\ \rightarrow \: \sf \: 12 {x}^{2} + 8x + 27x + 18 = 12 {x}^{2} + 44x + 9x + 33 \\ \\ \rightarrow \: \sf \: 12 {x}^{2} + 35x + 18 = 12 {x}^{2} + 53x + 33 \\ \\ \rightarrow \: \sf \: (12 {x}^{2} + 35x + 18) - (12 {x}^{2} + 53x + 33) = 0 \\ \\ \rightarrow \: \sf \: (12 {x}^{2}+ 35x + 18 - 12 {x}^{2} - 53x - 33 )= 0 \\ \\ \rightarrow \: \sf( - 18x - 15) = 0 \\ \\ \rightarrow\sf \: - 18x = 15 \\ \\ \rightarrow \: x = - \frac { \cancel15}{ \cancel18} \\ \\ \rightarrow \: \sf \: \boxed{x = \frac{5}{6}}$

Therefore:-

The value of x is 5/6.