Question

$\frac{2m+5}{3}=3m-10$

Answer 1

$\begin{array}{l}\\ \text{We have,}\\ \frac{2m+5}{3}=3m-10\\ \Rightarrow 2m+5=3(3m-10)\\ \Rightarrow 2m+5=9m-30\\ \Rightarrow 2m-9m=-30-5\left(\mathrm{T}\text{ransposing 9}\mathit{\text{m}}\text{to LHS and 5 to RHS}\right)\\ \Rightarrow -7m=-35\\ \Rightarrow m=\frac{-\sout{3}{\sout{5}}^5}{-{\sout{7}}^1}\\ \Rightarrow m=5\\ \\ \text{CHECK: Substituting}m=\text{5 in the given equation, we get:}\\ \\ \text{LHS=}\frac{2m+5}{3}\\ \text{=}\frac{2\times 5+5}{3}\\ \text{=}\frac{10+5}{3}\\ \text{=}\frac{\sout{1}{\sout{5}}^5}{{\sout{3}}^1}\\ \text{=5}\\ \\ \text{RHS=}3m-10\\ \text{=3}\times \text{5}-10\\ \text{=15}-10\\ \text{=5}\\ \text{∴ LHS=RHS}\\ \text{Hence,}x\text{=5 is a solution of the given equation}\text{.}\end{array}$