Question

Solve the following equation and verify the answer:

\[\frac{n}{4} - 5 = \frac{n}{6} + \frac{1}{2}\]

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.