# How do you solve the inequality 9x^2+16>=24x and write your answer in interval notation?

May 25, 2017

Solution: $x \in \mathbb{R}$ , In Interval notation: $\left(- \infty , \infty\right)$

#### Explanation:

$9 {x}^{2} + 16 \ge 24 x \mathmr{and} 9 {x}^{2} + 16 - 24 x \ge 0 \mathmr{and} 9 {x}^{2} - 24 x + 16 \ge 0$ or

${\left(3 x - 4\right)}^{2} \ge 0 \mathmr{and} \left(3 x - 4\right) \left(3 x - 4\right) \ge 0$. Critical point is $x = \frac{4}{3}$

At x =4/3 ; (3x-4)(3x-4) =0.On either side of x=4/3 ; (3x-4)(3x-4) >0 :. x in RR  , In Interval notation: $\left(- \infty , \infty\right)$

Solution: $x \in \mathbb{R}$ , In Interval notation: $\left(- \infty , \infty\right)$
graph{9x^2-24x+16 [-10, 10, -5, 5]} [Ans]