# How do you solve (3x - 5) ( x - 2 ) < 0 ?

Nov 7, 2015

$x \in \left(\frac{5}{3} , 2\right)$

#### Explanation:

$\left(3 x - 5\right) \left(x - 2\right)$ is the equation of a parabola
with x-intercepts at $\frac{5}{3}$ and $2$

If expanded into standard form the leading term is $3 {x}^{2}$

$\Rightarrow$ the leading term coefficient is positive

$\Rightarrow$ the parabola opens upward

$\Rightarrow$ the points between the x-intercepts are below the X-axis

$\Rightarrow$ the value of the parabola is $< 0$ when $x \in \left(\frac{5}{3} , 2\right)$