Question

Solve the linear equation

$x+7-\frac{8x}{3}=\frac{17}{6}-\frac{5x}{2}$

Answer 1

Solving the equation:

$x+7-\frac{8x}{3}=\frac{17}{6}-\frac{5x}{2}$

On combining the like terms, we obtain

$$\begin{gathered} x+7-\frac{8x}{3}=\frac{17}{6}-\frac{5x}{2} \\ \Rightarrow x-\frac{8x}{3}+\frac{5x}{2}=\frac{17}{6}-7 \\ \Rightarrow \frac{6x-16x+15x}{6}=\frac{17-42}{6} \\ \Rightarrow \frac{5x}{6}=\frac{-25}{6} \\ \Rightarrow x=\frac{-25}{6}\times \frac{6}{5} \\ \Rightarrow x=-5 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{5}$ is the solution of given equation.