Question

Solve each of the following equations and verify the answer in each case:
$\frac{n}{4}-5=\frac{n}{6}+\frac{1}{2}$

Answer 1

$\frac{n}{4}-5=\frac{n}{6}+\frac{1}{2}$
or, $\frac{n}{4}-\frac{n}{6}=\frac{1}{2}+5$ [Transposing n/6 to the L.H.S. and 5 to the R.H.S.]
or, $\frac{3n-2n}{12}=\frac{1+10}{2}$
or, $\frac{n}{12}=\frac{11}{2}$
or, $\frac{n}{12}\times 12=\frac{11}{2}\times 12$ [Dividing both the sides by 12]
or, n = 66
Verification:
Substituting n = 66 on both the sides:

L.H.S.:
$\frac{66}{4}-5=\frac{33}{2}-5=\frac{33-10}{2}=\frac{23}{2}=\frac{23}{2}R.H.S.:\frac{66}{6}+\frac{1}{2}=11+\frac{1}{2}=\frac{22+1}{2}=\frac{23}{2}$
L.H.S. = R.H.S.
Hence, verified.