Question

Find the value of $n$ in the following equation:
$\frac{2}{3}(4n-1)-(2n-\frac{1+n}{3})=\frac{1}{3}n+\frac{4}{3}$

• A. -$\frac{5}{4}$
• B. $\frac{5}{4}$
• C. -$\frac{5}{2}$
• D. $\frac{5}{2}$

Answer 1

The correct option is D $\frac{5}{2}$

Given expression:
$\frac{2}{3}(4n-1)-(2n-\frac{1+n}{3})=\frac{1}{3}n+\frac{4}{3}$

By taking the LCM,
$\frac{2}{3}(4n-1)-\frac{1}{3}(6n-1-n)=\frac{1}{3}n+\frac{4}{3}$

The denominator of all the terms are same.

So, by removing the denominator,
$2(4n-1)-(5n-1)=n+4$
$⟹$ $8n-2-5n+1=n+4$
$⟹$ $(8n-5n)+(-2+1)=n+4$
$⟹$ $3n-1=n+4$
$⟹$ $3n-n=4+1$
$⟹$ $2n=5$
$⟹$ $n=\frac{5}{2}$