Question

Find the value of $x$, if $\frac{1}{2}(x+1)+\frac{1}{2}(x-1)=\frac{5}{12}(x-2)$.

• A. $\frac{2}{7}$
• B. $\frac{1}{7}$
• C. $\frac{10}{7}$
• D. $-\frac{10}{7}$

Answer 1

The correct option is D $-\frac{10}{7}$

Given, $\frac{1}{2}(x+1)+\frac{1}{2}(x-1)=\frac{5}{12}(x-2)$.

Multiplying by $12$ on both sides, we get,

$\Rightarrow$ $6(x+1)+6(x-1)=5(x-2)$

$\Rightarrow$ $6x+6x+6-6=5x-10$ ...[By Distribution Law]

$\Rightarrow$ $12x=5x-10$

$\Rightarrow$ $10=-7x$ ...[Transposing $x$ terms to one side and simplifying]

$\Rightarrow$ $x=\frac{-10}{7}$.

Hence, option $D$ is correct.