Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}\frac{x+2}{x-2}=\frac{2}{3},\mathrm{then}x= \\ \left(\mathrm{a}\right)-10\left(\mathrm{b}\right)10\left(\mathrm{c}\right)\frac{4}{3}\left(\mathrm{d}\right)-\frac{4}{3} \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},\frac{x+2}{x-2}=\frac{2}{3} \\ \Rightarrow 3\left(x+2\right)=2\left(x-2\right)\left(\mathrm{By}\mathrm{cross}\mathrm{multiplication}\right) \\ \Rightarrow 3x+6=2x-4 \\ \Rightarrow 3x-2x=-6+4\left(\mathrm{By}\mathrm{transposing}2x\mathrm{to}\mathrm{LHS}\mathrm{and}6\mathrm{to}\mathrm{RHS}\right) \\ \therefore x=-10 \end{gathered}$$

Hence, the correct alternative is option (a).