Question

$\frac{9x+7}{2}-\left(x-\frac{x-2}{7}\right)=36$

Answer 1

$\begin{array}{l}\\ \text{We have:}\\ \frac{9x+7}{2}-(x-\frac{x-2}{7})=36\\ \Rightarrow \frac{9x+7}{2}-x+\frac{x-2}{7}=36\\ \Rightarrow \frac{7(9x+7)-14\times x+2\times (x-2)}{14}=36\\ \Rightarrow \frac{63x+49-14x+2x-4}{14}=36\\ \Rightarrow 51x+45=36\times 14\\ \Rightarrow 51x=504-45\\ \Rightarrow x=\frac{459}{51}\\ \Rightarrow x=9\\ \Rightarrow x=9\\ \text{CHECK: Substituting}x\text{= 9 in the given equation, we get:}\\ \\ \text{LHS=}\frac{9x+7}{2}-\left(x-\frac{x-2}{7}\right)\\ \text{=}\frac{9\times 9+7}{2}-\left(9-\frac{9-2}{7}\right)\\ \text{=}\frac{88}{2}-9+\frac{7}{7}\\ \text{=44}-9+1\\ \text{=36}\\ \text{RHS =36}\\ \\ \text{∴ LHS=RHS}\\ \text{Hence,}x\text{= 11 is a solution of the given equation}\text{.}\\ \text{Verified.}\end{array}$