# How do you solve the exponential inequality 9^(2x-3)<=9^(x+2)?

Dec 14, 2017

$x \le 5$

#### Explanation:

${9}^{2 x - 3} \le {9}^{x + 2}$

$\implies 2 x - 3 \le x + 2$

$\implies \left(2 x - 3\right) - \left(x + 2\right) \le 0$

$\implies x - 5 \le 0$

$\implies x \le 5$

So, we see that it's true for all the values of $x$ where $x$ is either less or equal to $5$.

Visually, all the shaded region in the graph below.

graph{x<=5}