Question

$0.5x+\frac{x}{3}=0.25x+7$

Answer 1

$\begin{array}{l}\\ \text{We have:}\\ 0.5x+\frac{x}{3}=0.25x+7\\ \Rightarrow \frac{1}{2}x+\frac{x}{3}=\frac{x}{4}+7\\ \Rightarrow \frac{x}{2}+\frac{x}{3}-\frac{x}{4}=7\\ \Rightarrow \frac{6x+4x-3x}{12}=7\\ \Rightarrow \frac{7x}{12}=7\\ \Rightarrow x=12\\ \\ \text{CHECK: Substituting}x\text{= 9 in the given equation, we get:}\\ \\ \text{LHS=}0.5x+\frac{x}{3}\\ \text{=}0.5\times 12+\frac{12}{3}\\ \text{=}\frac{1}{2}\times 12+4\\ \text{=6+4}\\ \text{=10}\\ \text{RHS=}0.25x+7\\ =0.25\times 12+7\\ =3+7\\ =10\\ \\ \text{∴ LHS=RHS}\\ \text{Hence,}x\text{= 12 is a solution of the given equation}\text{.}\\ \text{Verified.}\end{array}$