Solve the inequation: $\;$ $3x^2 - 7x + 4 \leq 0$
Given inequation: $\;$ $3x^2 - 7x + 4 \leq 0$
i.e. $\;$ $\left(3x - 4\right) \left(x - 1\right) \leq 0$
i.e. $\;$ $3x - 4 \leq 0 \; \cap \; x - 1 \geq 0$ $\;$ OR $\;$ $3x - 4 \geq 0 \; \cap \; x - 1 \leq 0$
i.e. $\;$ $x \leq \dfrac{4}{3} \; \cap \; x \geq 1$ $\implies$ $x \in \left[1, \dfrac{4}{3}\right]$
OR $\;$ $x \geq \dfrac{4}{3} \; \cap \; x \leq 1$ $\;$ which is not possible
$\therefore \;$ The solution is $\;$ $x \in \left[1, \dfrac{4}{3}\right]$