Question

5
$\frac{5}{4} (7x - 3) - (4x - \frac{1 - x}{2} ) = x - \frac{3}{2 }$
find the equation​

Answer 1

Given :

$\sf \dfrac{5}{4} (7x - 3) - \Bigg(4x - \dfrac{1 - x}{2} \Bigg) = x - \dfrac{3}{2 }$

To Find :

• Value of x = ?

Solution :

$\sf : \implies \dfrac{5}{4} (7x - 3) - \Bigg(4x - \dfrac{1 - x}{2} \Bigg) = x - \dfrac{3}{2}$

$\sf : \implies \dfrac{5 \times 7x}{4} - \dfrac{5 \times 3}{4} - \Bigg(\dfrac{8x}{2} - \dfrac{1 - x}{2} \Bigg) = \dfrac{2x}{2} - \dfrac{3}{2}$

$\sf : \implies \dfrac{35x}{4} - \dfrac{15}{4} - \Bigg(\dfrac{8x - (1-x)}{2} \Bigg) = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{35x}{4} - \dfrac{15}{4} - \Bigg(\dfrac{8x - 1 + x}{2} \Bigg) = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{35x}{4} - \dfrac{15}{4} - \Bigg(\dfrac{9x - 1}{2} \Bigg) = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{35x}{4} - \dfrac{15}{4} - \dfrac{9x - 1}{2} = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{35x}{4} - \dfrac{15}{4} - \dfrac{(9x - 1) \times 2}{2 \times 2} = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{35x}{4} - \dfrac{15}{4} - \dfrac{18x - 2}{4} = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{35x - 15 - (18x - 2)}{4} = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{35x - 15 - 18x + 2}{4} = \dfrac{2x - 3}{2}$

$\sf : \implies \dfrac{17x - 13}{4} = \dfrac{2x - 3}{2}$

By cross multiply :

$\sf : \implies (17x - 13) \times 2 = (2x - 3) \times 4$

$\sf : \implies 34x - 26 = 8x - 12$

$\sf : \implies 34x - 26 - 8x + 12 = 0$

$\sf : \implies 26x - 14 = 0$

$\sf : \implies 26x = 14$

$\sf : \implies x = \cancel{\dfrac{14}{26}}$

$\sf : \implies x = \dfrac{7}{13}$

$\Large \underline{\boxed{\sf{ x = \dfrac{7}{13} }}}$

$\bf Hence, \: value \: of \: x = \dfrac{7}{13}$

Answer 2

Answer:

The answer of your question is x = 7/13

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