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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
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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.
\(x>3\) \(-x>3\)

 

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

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