Question

$2x-\frac{1}{3}=\frac{1}{5}-x$

Answer 1

$$\begin{gathered} \begin{array}{l}\\ \text{We have:}\\ 2x-\frac{1}{3}=\frac{1}{5}-x\\ \Rightarrow 2x+x=\frac{1}{5}+\frac{1}{3}\\ \Rightarrow 3x=\frac{3\times 1+5\times 1}{15}\\ \Rightarrow 3x=\frac{3+5}{15}\\ \Rightarrow 3x=\frac{8}{15}\\ \Rightarrow x=\frac{8}{15\times 3}\\ \Rightarrow x=\frac{8}{45}\\ \\ \text{CHECK: Substituting}x\text{=}\frac{8}{45}\text{in the given equation, we get:}\\ \\ \text{LHS:}2x-\frac{1}{3}\\ \text{=2}\times \frac{8}{45}-\frac{1}{3}\\ \text{=}\frac{16}{45}-\frac{1}{3}\\ \text{=}\frac{16\times 1-15\times 1}{45}\\ \text{=}\frac{16-15}{45}\\ \text{=}\frac{1}{45}\\ \\ \\ \mathrm{RHS}:\frac{1}{5}-x\\ \text{=}\frac{1}{5}-\frac{8}{45}\\ \text{=}\frac{1\times 9-1\times 8}{45}\\ \text{=}\frac{9-8}{45}\\ \text{=}\frac{1}{45}\\ \text{∴ LHS=RHS}\end{array} \\ \mathrm{Hence},x\text{=}\frac{8}{45}\text{is a solution of the given equation}\text{.} \end{gathered}$$