Question

Mark the correct alternative in each of the following:

If $\frac{x}{2}+\frac{1}{3}=1$, then x =

(a) $\frac{3}{4}$ (b) $\frac{4}{3}$ (c) $-\frac{3}{4}$ (d) $\frac{-4}{3}$

Answer 1

$$\begin{gathered} \frac{x}{2}+\frac{1}{3}=1 \\ \Rightarrow \frac{x}{2}=1-\frac{1}{3} \\ \Rightarrow \frac{x}{2}=\frac{3\times 1-1}{3} \\ \Rightarrow \frac{x}{2}=\frac{3-1}{3} \\ \Rightarrow \frac{x}{2}=\frac{2}{3} \end{gathered}$$
$$\begin{gathered} \Rightarrow \frac{2x}{2}=\frac{2\times 2}{3}\left(\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}2\right) \\ \Rightarrow x=\frac{4}{3} \end{gathered}$$

Hence, the correct answer is option (b).