Question

pls help in question no 8.....it's of linear equations.....we have to solve it n find d value of x

Answer 1

Hi there !

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Given :

$\bold{ \large{ \frac{2x - \frac{3}{4} }{3x + \frac{4}{5} } = \frac{1}{5} }}$

Now, on cross - multiplying, we get ;

$\bold{ { \frac{2x - \frac{3}{4} }{3x + \frac{4}{5} } = \frac{1}{5} }} \\ \\ \bold{3x + \frac{4}{5} = 5(2x - \frac{3}{4}) } \\ \\ \bold{3x + \frac{4}{5} = 10x - \frac{15}{4} } \\ \\ \bold{ \frac{15x + 4}{5} = \frac{40x - 15}{4} } \\ \\ \bold{on \: cross \: multiplying..} \\ \\ \bold{4(15x + 4) = 5(40x - 15)} \\ \\ \bold{60x + 16 = 200x - 75} \\ \\ \bold{60x - 200x = - 75 - 16} \\ \\ \bold{ \cancel- 140x = \cancel- 91} \\ \\ \bold{140x = 91} \\ \\ \bold{x = \frac{91}{140} } \\ \\ \therefore \: \bold{x = 0.65}$

VERIFICATION ;

$\bold{ { \frac{2x - \frac{3}{4} }{3x + \frac{4}{5} } = \frac{1}{5} }} \\ \\ \\ \bold{ \frac{2 \times 0.65 - \frac{3}{4} }{3 \times 0.65 + \frac{4}{5} } = \frac{1}{5} } \\ \\ \\ \bold{ \frac{1.3 - \frac{3}{4} }{1.95 + \frac{4}{5} } } = \frac{1}{5} \\ \\ \\ \bold{ \frac{ \frac{5.2 - 3}{4} }{ \frac{9.75 + 4}{5} } = \frac{1}{5} } \\ \\ \\ \bold{ \frac{ \frac{2.2}{4} }{ \frac{13.75}{5} } = \frac{1}{5} } \\ \\ \\ \bold{ \frac{2.2 \times 5}{ 13.75 \times 4} = \frac{1}{5}} \\ \\ \\ \bold{ \frac{11}{55} = \frac{1}{5} } \\ \\ \\ \bold{ \frac{1}{5} = \frac{1}{5} } \\ \\ \\ \therefore \: \bold{LHS \: = \: RHS}.$

Hence,

The answer is x = 0.65.

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Thanks for the question !