Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}2x-\frac{3}{2}=5x+\frac{3}{4},\mathrm{then}x= \\ \left(\mathrm{a}\right)\frac{3}{4}\left(\mathrm{b}\right)-\frac{3}{4}\left(\mathrm{c}\right)\frac{4}{3}\left(\mathrm{d}\right)-\frac{4}{3} \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},2x-\frac{3}{2}=5x+\frac{3}{4} \\ \Rightarrow 2x-5x=\frac{3}{2}+\frac{3}{4}\left(\mathrm{By}\mathrm{transposing}-\frac{3}{2}\mathrm{to}\mathrm{RHS}\mathrm{and}5x\mathrm{to}\mathrm{LHS}\right) \\ \Rightarrow -3x=\frac{6}{4}+\frac{3}{4} \\ \Rightarrow -3x=\frac{6+3}{4} \\ \Rightarrow x=\frac{9}{4\times \left(-3\right)}\left(\mathrm{By}\mathrm{transposing}-3\mathrm{to}\mathrm{RHS}\right) \\ \Rightarrow x=\frac{3}{4\times \left(-1\right)} \\ \Rightarrow x=\frac{3}{-4} \\ \therefore x=-\frac{3}{4} \end{gathered}$$

Hence, the correct alternative is option (b).