Question

The value of $x$ satisfying $\frac{x-4}{7}-\frac{x+4}{5}=\frac{x+3}{7}$ is ______.

Answer 1

Given,

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

$\Rightarrow \frac{5(x-4)-7(x+4)}{7\times 5}=\frac{x+3}{7}$

$\Rightarrow 5x-20-7x-28=\frac{x+3}{7}(7\times 5)$

$\Rightarrow -2x-48=5(x+3)$

$\Rightarrow -2x-48=5x+15$

$\Rightarrow -48-15=5x+2x$ ....[Transposing $x$ terms to one side]

$\Rightarrow 7x=-63$

$\Rightarrow x=\frac{-63}{7}=-9$.

Hence, the correct answer is $-9$.