Question

$\frac{2}{3}x=\frac{3}{8}x+\frac{7}{12}$

Answer 1

$\begin{array}{l}\\ \text{We have:}\\ \frac{2}{3}x=\frac{3}{8}x+\frac{7}{12}\\ \Rightarrow \frac{2}{3}x-\frac{3}{8}x=\frac{7}{12}\left(\mathrm{T}\text{ransposing}\frac{3}{8}x\text{to LHS}\right)\\ \Rightarrow \left(\frac{2\times 8-3\times 3}{24}\right)x=\frac{7}{12}\\ \Rightarrow \left(\frac{16-9}{24}\right)x=\frac{7}{12}\\ \Rightarrow \frac{7}{24}x=\frac{7}{12}\\ \Rightarrow x=\frac{{\sout{7}}^1}{\sout{1}{\sout{2}}^1}\times \frac{\sout{2}{\sout{4}}^2}{{\sout{7}}^1}\\ \Rightarrow x=2\\ \\ \text{CHECK: Substituting}x\text{=2 in the given equation, we get:}\\ \\ \text{LHS=}\frac{2}{3}x\\ \text{=}\frac{2}{3}\times 2\\ \text{=}\frac{4}{3}\\ \\ \text{RHS=}\frac{3}{8}x+\frac{7}{12}\\ \text{=}\frac{3}{8}\times 2+\frac{7}{12}\\ \text{=}\frac{6}{8}+\frac{7}{12}\\ \text{=}\frac{6\times 3+7\times 2}{24}\\ \text{=}\frac{18+14}{24}\\ \text{=}\frac{\sout{3}{\sout{2}}^4}{\sout{2}{\sout{4}}^3}\\ =\frac{4}{3}\\ \begin{array}{l}\text{∴ LHS=RHS}\\ \text{Hence,}x\text{=2 is a solution of the given equation}\text{.}\end{array}\end{array}$