Question

The value of $n$ that satisfies the equation $\frac{3(n-2)+5}{4}=\frac{11-(7-n)}{6}$ is:

• A. $-\frac{1}{11}$
• B. $\frac{5}{11}$
• C. $1$
• D. $\frac{11}{7}$

Answer 1

The correct option is D $\frac{11}{7}$

Given, $\frac{3(n-2)+5}{4}=\frac{11-(7-n)}{6}$

$\Rightarrow$ $\frac{3n-6+5}{4}=\frac{11-7+n}{6}$ ...[By Distribution Law]

$\Rightarrow \frac{3n-1}{4}=\frac{n+4}{6}$ ...[On simplifying]

$\Rightarrow 18n-6=4n+16$ …[Cross-multiplying the denominators].

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

$\Rightarrow 18n-4n=6+16$

$\Rightarrow 14n=22$

$\Rightarrow n=\frac{22}{14}=\frac{11}{7}$.

Hence, option $D$ is correct.