Find the value of x, if (3x - 7) : (4x + 3) is the sub-triplicate ratio of 8 : 27

According to question,

$\Rightarrow \dfrac{3x - 7}{4x + 3} = \dfrac{\sqrt[3]{8}}{\sqrt[3]{27}} \\[1em] \Rightarrow \dfrac{3x - 7}{4x + 3} = \dfrac{2}{3} \\[1em] \Rightarrow 3(3x - 7) = 2(4x + 3) \\[1em] \Rightarrow 9x - 21 = 8x + 6 \\[1em] \Rightarrow 9x - 8x = 6 + 21 \\[1em] \Rightarrow x = 27.$

Hence, x = 27.