Solve the following equation and check your answer:

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

We have:

$\phantom{=} \dfrac{2x + 3}{3 +x} = \dfrac{3}{2} \\[1em] \Rightarrow 2(2x + 3) = 3(3 + x) \quad \text{[By cross multiplication]} \\[1em] \Rightarrow 4x + 6 = 9 + 3x \\[1em] \Rightarrow 4x - 3x = 9 - 6 \quad \text{[Transposing +6 to RHS and +3x to LHS]} \\[1em]$

∴ x = 3

Check:

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

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

= $\dfrac{9}{6}$

= $\dfrac{3}{2}$

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

Hence, LHS = RHS.