Solve the following equation and check your answer:

$\dfrac{x + 5}{2} + \dfrac{x}{3} = 20$

We have:

$\phantom{=} \dfrac{x + 5}{2} + \dfrac{x}{3} = 20 \\[1em] \Rightarrow \dfrac{3(x + 5) + 2x}{6} = 20 \\[1em] \Rightarrow 3x + 15 + 2x = 20 \times 6 \\[1em] \Rightarrow 5x + 15 = 120 \\[1em] \Rightarrow 5x = 120 - 15 \quad \text{[Transposing +15 to RHS]} \\[1em] \Rightarrow 5x = 105 \\[1em] \Rightarrow x = \dfrac{105}{5} \\[1em]$

∴ x = 21

Check:

LHS = $\dfrac{x + 5}{2} + \dfrac{x}{3}$

= $\dfrac{21 + 5}{2} + \dfrac{21}{3}$

= 13 + 7

= 20

RHS = 20

Hence, LHS = RHS.