Question

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

Answer 1

Transpose $\frac{5x}{2}$ to LHS and $7$ to RHS
We get,

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

$LHS:x+\frac{5x}{2}-\frac{8x}{3}$

LCM of $2$ and $6\Rightarrow 6$

$LHC\Rightarrow x+\frac{5x}{2}-\frac{8x}{3}\Rightarrow \frac{6x+15x-16x}{6}\Rightarrow \frac{5x}{6}$ ..... (1)

$RHS:\frac{17}{6}-7\Rightarrow \frac{17-42}{6}=\frac{-25}{6}$ ..... (2)

$LHS=RHS$ (equate (1) and (2))

$\frac{5x}{6}=\frac{-25}{6}$

$x=-5$