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

AdamTaurus  Sep 8, 2017

1+0 Answers


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


Divide by -1 on both sides. Remember that doing so flips the inequality sign. That's easy to forget!
\(x>3\) \(x<-3\)


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

19 Online Users

New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy