Question

$\frac{y-1}{3}-\frac{y-2}{4}=1$

Answer 1

$\begin{array}{l}\\ \text{We have:}\\ \frac{y-1}{3}-\frac{y-2}{4}=1\\ \Rightarrow \frac{4(y-1)-3(y-2)}{12}=1\\ \Rightarrow \left(\frac{4y-4-3y+6}{12}\right)=1\\ \Rightarrow \left(\frac{y+2}{12}\right)=1\\ \Rightarrow y+2=1\times 12\\ \Rightarrow y=12-2\\ \Rightarrow y=10\\ \text{CHECK: Substituting y=10 in the given equation, we get:}\\ \\ \text{LHS=}\frac{y-1}{3}-\frac{y-2}{4}\\ \text{=}\frac{4(y-1)-3(y-2)}{12}\\ \text{=}\left(\frac{y+2}{12}\right)\\ \text{=}\left(\frac{10+2}{12}\right)\\ \text{=}\frac{\sout{1}{\sout{2}}^1}{\sout{1}{\sout{2}}^1}\\ \text{=1}\\ \\ \text{RHS=1}\\ \text{∴ LHS=RHS}\\ \text{Hence, y=10 is a solution of the given equation}\text{.}\end{array}$