The line $\dfrac{3x}{5} - \dfrac{2y}{3} + 1 = 0$ contains the point (m, 2m - 1); calculate the value of m.

Since, (m, 2m - 1) lies on the line $\dfrac{3x}{5} - \dfrac{2y}{3} + 1 = 0$, it will satisfy the equation.

Substituting x = m, y = 2m - 1 in the equation $\dfrac{3x}{5} - \dfrac{2y}{3} + 1 = 0$ we get,

$\Rightarrow \dfrac{3m}{5} - \dfrac{2(2m - 1)}{3} + 1 = 0 \\[1em] \Rightarrow \dfrac{(3m \times 3) - [5 \times 2(2m - 1)] + 15}{15} = 0 \\[1em] \Rightarrow 9m - 10(2m - 1) + 15 = 0 \\[1em] \Rightarrow 9m - 20m + 10 + 15 = 0 \\[1em] \Rightarrow -11m = -25 \\[1em] \Rightarrow 11m = 25 \\[1em] \Rightarrow m = \dfrac{25}{11} = 2\dfrac{3}{11}.$

Hence, m = $2\dfrac{3}{11}.$