Question

Solve: $\frac{x-6}{5}+\frac{x-4}{3}=8-\frac{x-2}{7}$.

• A. $-16$
• B. $16$
• C. $8$
• D. $-8$

Answer 1

The correct option is B $16$

Given,

$\frac{x-6}{5}+\frac{x-4}{3}=8-\frac{x-2}{7}$.

Multiplying throughout by the LCM of denominator, i.e., LCM of $5,3,7=$ $105$, we get,
$21(x-6)+35(x-4)=105\times 8-15(x-2)$
$⟹$ $21x-126+35x-140=840-15x+30$ ...[By Distribution Law]
$⟹$ $56x-266=870-15x$ ...[On simplifying].

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

$⟹$ $56x+15x=266+870$
$⟹$ $71x=1136$
$⟹$ $x=16$.

Hence, option $B$ is correct.