Question

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

• A. $\frac{-29}{5}$
• B. $\frac{-1}{6}$
• C. $\frac{1}{5}$
• D. $\frac{29}{6}$

Answer 1

The correct option is A $\frac{-29}{5}$

The given equation is,
$\frac{x-4}{7}+\frac{x+4}{5}=\frac{x-3}{5}$.
$\Rightarrow \frac{5(x-4)+7(x+4)}{35}=\frac{x-3}{5}\Rightarrow \frac{5x-20+7x+28}{35}=\frac{x-3}{5}\Rightarrow \frac{12x+8}{35}=\frac{x-3}{5}\Rightarrow 12x+8=\frac{x-3}{5}\times 35$
$\Rightarrow 12x+8=7(x-3)\Rightarrow 12x+8=7x-21\Rightarrow 12x-7x=-21-8\Rightarrow 5x=-29\Rightarrow x=\frac{-29}{5}$

Hence, the value of $x$ is $\frac{-29}{5}$