Question

Solve the equation: $\frac{2}{7}-\frac{(x+8)}{4}=\frac{3(x-3)}{5}-\frac{3}{2}$.

• A. no solutions
• B. $0$
• C. $\frac{17}{111}$
• D. $\frac{37}{119}$
• E. $\frac{222}{119}$

Answer 1

The correct option is E $\frac{222}{119}$

Given, $\frac{2}{7}-\frac{(x+8)}{4}=\frac{3(x-3)}{5}-\frac{3}{2}$

$\Rightarrow \frac{8-7x-56}{28}=\frac{6x-18-15}{10}$ …[Taking LCM of the denominators]

$\Rightarrow \frac{-7x-48}{14}=\frac{6x-33}{5}$ ...[On simplifying]

$\Rightarrow 5(-7x-48)=14(6x-33)$ …[Cross-multiplying the denominators]

$\Rightarrow -35x-240=84x-462$ ...[By Distribution Law].

Transposing $x$ terms to one side, we get,

$\Rightarrow -35x-84x=-462+240$

$\Rightarrow -119x=-222$

$\Rightarrow x=\frac{222}{119}$.

Hence, option $E$ is correct.