The sqrt(16) = 4, but the equation x^{2} = 16 has two solutions, x = 4, -4. The reason for this fact is the fact that sqrt(x^{2}) = the absolute value of x. Using this fact, solve the following inequality algebraically:

x^{2}-9 > 0

AdamTaurus
Sep 8, 2017

#1**+1 **

Inequalities can be tricky things, so let's solve them. In this problem, we will solve for x in the equation \(x^2-9>0\):

\(x^2-9>0\) | Add 9 to both sides of the inequality. | ||

\(x^2>9\) | Take the square root of both sides. | ||

\(|x|>\sqrt{9}\) | |||

\(|x|>3\) | The absolute value splits the solutions into 2 inequalities. Solve them separately. | ||

| Divide by -1 on both sides. Remember that doing so flips the inequality sign. That's easy to forget! | ||

| Npw, let's combine this into a compound inequality, if possible. Unfortunately, in this case, it is not. | ||

Therefore, x must either be greater than 3 or less than -3.

TheXSquaredFactor
Sep 9, 2017