Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}\frac{x-2}{3}=\frac{2x-1}{3}-1,\mathrm{then}x= \\ \left(\mathrm{a}\right)2\left(\mathrm{b}\right)4\left(\mathrm{c}\right)6\left(\mathrm{d}\right)8 \end{gathered}$$

Answer 1

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

Hence, the correct alternative is option (a).