Question

5x-4 /8 -(x-3) /4 =(x+6)/4 solve it the equation

Answer 1

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Answer 2

Hi there!

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$\mathsf{ \frac{5x - 4}{8} - \frac{x - 3}{4} = \frac{x + 6}{4} } \\ \\ \implies{ \mathsf{ \frac{5x - 4 - 2(x - 3)}{8} = \frac{x + 6}{4} }} \\ \\ \implies{ \mathsf{ \frac{5x - 4 - 2x + 6}{8} =\frac{x + 6}{4} }} \\ \\ \implies{ \mathsf{ \frac{3x + 2}{8} = \frac{x + 6}{4} }} \\ \\ \bold{on \: cross \: multiplying..} \\ \\ \implies{ \mathsf{4(3x + 2) = 8(x + 6)}} \\ \\ \implies{ \mathsf{12x + 8 = 8x + 48}} \\ \\ \implies{ \mathsf{12x - 8x = 48 - 8}} \\ \\ \implies{ \mathsf{4x = 40}} \\ \\ \implies{ \mathsf{x = \frac{ \cancel{40} \: {}^{10} }{ \cancel{ \: 4}} }} \\ \\ \therefore{ \mathsf{x = 10}}$

$\underline{\bold{verificantion}}$

Putting the value of x = 10 ;

$\mathsf{ \frac{5x - 4}{8} - \frac{x - 3}{4} = \frac{x + 6}{4} } \\ \\\mathsf{ \frac{5 \times 10 - 4}{8} - \frac{10 - 3}{4} = \frac{10 + 6}{4} } \\ \\ \mathsf{ \frac{50 - 4}{8} - \frac{10 - 3}{4} = \frac{10 + 6}{4} } \\ \\ \mathsf {\frac{46}{8} - \frac{7}{4} = \frac{16}{4} } \\ \\ \mathsf{\frac{46 - 14}{8} = \frac{16}{4} } \\ \\ \mathsf{ \frac{36}{8} = \frac{16}{4} } \\ \\ \mathsf{ \frac{16}{4} = \frac{16}{4} } \\ \\ \mathsf{4 = 4} \\ \\ \therefore \bold{ lhs = rhs}$

Hence, the value of x is 10.

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Thanks for the question!

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