Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}\frac{x}{6}+\frac{x}{4}=\frac{x}{2}+\frac{3}{4},\mathrm{then}x= \\ \left(\mathrm{a}\right)9\left(\mathrm{b}\right)6\left(\mathrm{c}\right)-9\left(\mathrm{d}\right)4 \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},\frac{x}{6}+\frac{x}{4}=\frac{x}{2}+\frac{3}{4} \\ \Rightarrow \frac{x}{6}+\frac{x}{4}-\frac{x}{2}=\frac{3}{4}\left(\mathrm{By}\mathrm{transposing}\frac{x}{2}\mathrm{to}\mathrm{LHS}\right) \\ \Rightarrow \frac{2x}{12}+\frac{3x}{12}-\frac{6x}{12}=\frac{3}{4} \\ \Rightarrow \frac{2x+3x-6x}{12}=\frac{3}{4} \\ \Rightarrow \frac{-x}{12}=\frac{3}{4} \\ \Rightarrow -x\times 4=3\times 12\left(\mathrm{By}\mathrm{cross}\mathrm{multiplication}\right) \\ \Rightarrow -4x=36 \\ \Rightarrow x=\frac{36}{-4} \\ \therefore x=-9 \end{gathered}$$

Hence, the correct alternative is option (c).