Question

Choose the right answer from the options given after every question.

The solution of the equation 3x $-\frac{1}{2}=\frac{5}{2}+x$ is ...................

(i) $\frac{5}{3}$ (ii) $\frac{7}{2}$ (iii) 4 (iv) $\frac{3}{2}$

Answer 1

$$\begin{gathered} 3x-\frac{1}{2}=\frac{5}{2}+x \\ \Rightarrow 3x-x-\frac{1}{2}=\frac{5}{2}+x-x \\ \Rightarrow 2x-\frac{1}{2}+\frac{1}{2}=\frac{5}{2}+\frac{1}{2} \end{gathered}$$
$$\begin{gathered} \Rightarrow 2x=\frac{5}{2}+\frac{1}{2} \\ \Rightarrow 2x=3 \\ \Rightarrow x=\frac{3}{2} \end{gathered}$$
Hence, the correct option is (iv).