# How do you solve 13x^2-5x<=0?

Aug 12, 2016

Solve as a regular quadratic and then select test points.

$13 {x}^{2} - 5 x = 0$

$x \left(13 x - 5\right) = 0$

$x = 0 \mathmr{and} \frac{5}{13}$

$\textcolor{b l u e}{\text{Test point 1"-> "-1}}$

13(-1)^2 - 5(-1) ≤^? 0

18≤^O/ 0

This inequality is obviously not true, so let's go on to test point $2$.

color(red)("Test point 2" -> "1/4"

13(1/4)^2 - 5(1/4) <=^? 0

$- 0.4375 \le 0$

Hence, the interval that is the solution to this inequality $0 \le x \le \frac{5}{13}$.

On a number line, the solution would be the turquoise rectangle.

Hopefully this helps!