Question 4

Explanation

To solve this inequality, we need to factor it first.

Let $u = 9^x$, so the inequality becomes

Factor the quadratic equation

Substitute back $u = 9^x$

Find the values of $x$ when the expression equals zero

1. $9^x = 1 \Rightarrow 9^x = 9^0 \Rightarrow x = 0$
2. $9^x = 9 \Rightarrow 9^x = 9^1 \Rightarrow x = 1$

Using a number line, we can determine the regions that satisfy the inequality

For $x < 0$, both factors are negative, so the result is positive

For $0 < x < 1$, one factor is positive and one is negative, so the result is negative

For $x > 1$, both factors are positive, so the result is positive

Therefore, the solution set is $\{x < 0 \text{ or } x > 1, x \in \mathbb{R}\}$