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.