Solve the following equation and check your answer:

$\dfrac{2x}{3} + 4x = 42$

We have:

$\phantom{=} \dfrac{2x}{3} + 4x = 42 \\[1em] \Rightarrow \dfrac{2x + 12x}{3} = 42 \\[1em] \Rightarrow 2x + 12x = 42 \times 3 \\[1em] \Rightarrow 14x = 126 \\[1em] \Rightarrow x = \dfrac{126}{14}$

∴ x = 9

Check:

LHS = $\dfrac{2x}{3} + 4x$

= $\dfrac{2(9)}{3} + 4(9)$

= $6 + 36$

= $42$

RHS = $42$

Hence, LHS = RHS.