Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}\frac{x}{2}-4=\frac{x}{3}-1,\mathrm{then}x= \\ \left(\mathrm{a}\right)3\left(\mathrm{b}\right)6\left(\mathrm{c}\right)18\left(\mathrm{d}\right)2 \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},\frac{x}{2}-4=\frac{x}{3}-1 \\ \Rightarrow \frac{x}{2}-\frac{x}{3}=4-1\left(\mathrm{By}\mathrm{transposing}\frac{x}{3}\mathrm{to}\mathrm{LHS}\mathrm{and}-4\mathrm{to}\mathrm{RHS}\right) \\ \Rightarrow \frac{3x}{6}-\frac{2x}{6}=3 \\ \Rightarrow \frac{3x-2x}{6}=3 \\ \Rightarrow \frac{x}{6}=3 \\ \Rightarrow x=3\times 6\left(\mathrm{By}\mathrm{transposing}6\mathrm{to}\mathrm{RHS}\right) \\ \therefore x=18 \end{gathered}$$

Hence, the correct alternative is option (c).