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

 Sep 8, 2017

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. 

 Sep 9, 2017

14 Online Users


New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.