Question

$\frac{2}{7}(x-9)+\frac{x}{3}=3$

Answer 1

$\begin{array}{l}\\ \text{We have:}\\ \Rightarrow \frac{2}{7}(x-9)+\frac{x}{3}=3\\ \Rightarrow \frac{2\times 3(x-9)+7x}{21}=3\\ \Rightarrow 6(x-9)+7x=3\times 21\\ \Rightarrow 6x-54+7x=63\\ \Rightarrow 13x=63+54\\ \Rightarrow 13x=117\\ \Rightarrow x=9\\ \\ \text{CHECK: Substituting}x\text{=9 in the given equation we get}\text{.}\\ \\ \text{LHS=}\frac{2}{7}(x-9)+\frac{x}{3}\\ \text{=}\frac{2}{7}(9-9)+\frac{x}{3}\\ \text{=0+}\frac{9}{3}\\ \text{=}\frac{9}{3}\\ \text{=3}\\ \text{RHS=3}\\ \therefore \mathrm{LHS}=\mathrm{RHS}\\ \text{Hence,}x\text{=9 is a solution of the given equation}\text{.}\end{array}$