+895 The sqrt(16) = 4, but the equation x2 = 16 has two solutions, x = 4, -4. The reason for this fact is the fact that sqrt(x2) = the absolute value of x. Using this fact, solve the following inequality algebraically:
x2-9 > 0
+2446 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.
