Question

Solve the given equation:

$\frac{2x+7}{5}-\frac{3x+11}{2}=\frac{2x+8}{3}-5$

Answer 1

Take the L.C.M of the denominators on both sides of the equation and then simplify

The given equation is:

$\frac{2x+7}{5}-\frac{3x+11}{2}=\frac{2x+8}{3}-5$

Taking L.C.M. on LHS and RHS, we obtain

$$\begin{gathered} \frac{2(2x+7)-5(3x+11)}{10}=\frac{2x+8-3\left(5\right)}{3}[\because \text{LCM}(2,5)=10and\text{LCM}(3,1)=3] \\ \Rightarrow \frac{4x+14-15x-55}{10}=\frac{2x+8-15}{3} \\ \Rightarrow \frac{-11x-41}{10}=\frac{2x-7}{3} \\ \Rightarrow 3(-11x-41)=10(2x-7) \\ \Rightarrow -33x-123=20x-70 \\ \Rightarrow -33x-20x=-70+123 \\ \Rightarrow -53x=53 \\ \Rightarrow x=\frac{-53}{53} \\ \Rightarrow x=-1 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{1}$ is the solution of the given equation.