Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}2x+\frac{5}{3}=\frac{1}{4}x+4,\mathrm{then}x= \\ \left(\mathrm{a}\right)3\left(\mathrm{b}\right)4\left(\mathrm{c}\right)\frac{3}{4}\left(\mathrm{d}\right)\frac{4}{3} \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},2x+\frac{5}{3}=\frac{1}{4}x+4 \\ \Rightarrow 2x-\frac{1}{4}x=4-\frac{5}{3}\left(\mathrm{By}\mathrm{transposing}\frac{5}{3}\mathrm{to}\mathrm{RHS}\mathrm{and}\frac{1}{4}x\mathrm{to}\mathrm{LHS}\right) \\ \Rightarrow \frac{2x}{1}-\frac{x}{4}=\frac{4}{1}-\frac{5}{3} \\ \Rightarrow \frac{8x}{4}-\frac{x}{4}=\frac{12}{3}-\frac{5}{3} \\ \Rightarrow \frac{8x-x}{4}=\frac{12-5}{3} \\ \Rightarrow \frac{7x}{4}=\frac{7}{3} \\ \Rightarrow 7x\times 3=4\times 7\left(\mathrm{By}\mathrm{cross}\mathrm{multiplication}\right) \\ \Rightarrow 21x=28 \\ \Rightarrow x=\frac{28}{21} \\ \therefore x=\frac{4}{3} \end{gathered}$$

Hence, the correct alternative is option (d).