Question

$\: \dfrac{x - 4}{7} - \dfrac{x + 4}{5} = \dfrac{x + 3}{7}$​

Answer 1

To Find :-

• Value of x

Solution :-

Given,

• $\sf \: \dfrac{x - 4}{7} - \dfrac{x + 4}{5} = \dfrac{x + 3}{7}$

Here,

$\sf \: \dfrac{x - 4}{7} - \dfrac{x + 4}{5} = \dfrac{x + 3}{7}$

$:\implies \: \sf \: \dfrac{x - 4}{7} = \dfrac{x + 3}{7} + \dfrac{x + 4}{5}$

$:\implies \: \sf \: \dfrac{x - 4}{7} = \dfrac{5x + 15 + 7x + 28}{35}$

$:\implies \: \sf \: \dfrac{x - 4}{7} = \dfrac{12x + 43}{35}$

$:\implies \: \sf \: 35( x - 4) = 7(12x + 43)$

$: \implies \: \sf \: 35 x - 140 = 84x + 301$

$:\implies \: \sf 84x - 35x = - 301 - 140$

$:\implies \: \sf 49x = - 441$

$:\implies \: \sf x = \dfrac{ - 441}{49}$

$:\implies{\underline{\boxed{\frak{\pink{x = -9}}}}}\;\bigstar$

$\boxed {\sf {\purple {Value\ of\ x\ is\ -9.}}}$

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Answer 2

$\large\bf{\underline{\underline{Question:-}}}$

Solve x :

$\: \dfrac{x - 4}{7} -\dfrac{x + 4}{5} = \dfrac{x + 3}{7}$

$\large\bf{\underline{\underline{Solution:-}}}$

$\: \dfrac{x - 4}{7} - \dfrac{x + 4}{5} = \dfrac{x + 3}{7}$

$\implies \dfrac{5(x - 4) - 7(x + 4)}{35} = \dfrac{x + 3}{7}$

$\implies \: 5(x - 4) - 7(x + 4) = \dfrac{(x + 3) \cancel{35}}{\cancel{7}}$

$\implies \: \cancel{5x} - 20 - 7x - 28 = \cancel{5x} + 15$

$\implies \: - 7x = 15 + 48$

$\implies \: x = \dfrac{63}{-7}$

$\implies \: x = - \dfrac{\cancel{63}}{\cancel{7}}$

$\Large\therefore{\boxed{x = - 9}}$

$\pink{Hope \: it \: helps}$