Solve the following equation and check your answer:

$\dfrac{8 - 3x}{5x + 31} = \dfrac{2}{3}$

We have:

$\phantom{=} \dfrac{8 - 3x}{5x + 31} = \dfrac{2}{3} \\[1em] \Rightarrow 3(8 - 3x) = 2(5x + 31) \quad \text{[By cross multiplication]} \\[1em] \Rightarrow 24 - 9x = 10x + 62 \\[1em] \Rightarrow 24 - 62 = 10x + 9x \quad \text{[Transposing -9x to RHS and +62 to LHS]} \\[1em] \Rightarrow -38 = 19x \\[1em] \Rightarrow x = \dfrac{-38}{19} \\[1em]$

∴ x = -2

Check:

LHS = $\dfrac{8 - 3x}{5x + 31}$

= $\dfrac{8 - 3(-2)}{5(-2) + 31}$

= $\dfrac{14}{21}$

= $\dfrac{2}{3}$

RHS = $\dfrac{2}{3}$

Hence, LHS = RHS.