Question

solve each inequality. graph the solution set and write it in interval notation.
|x| > 8

graph the inequality. choose the correct graph below
a.
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
b.
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
c.
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
d.
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
e.
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
f.
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| > a\) (where \(a>0\)), the solution is \(x < -a\) or \(x > a\). Here, \(a = 8\), so we have \(x < - 8\) or \(x > 8\).

Step2: Analyze the graphs

• Option A: Shows closed circles at -8 and 8, which would be for \(|x| = 8\) or inclusive inequalities, not \(|x| > 8\).
• Option B: Shows a closed circle at -8 and a line to the right, but it should also have a part for \(x < -8\), so incorrect.
• Option C: Has an open parenthesis (since \(x < -8\) and \(x > 8\) are strict inequalities, open circles) with arrows to the left of -8 and right of 8, which matches \(x < -8\) or \(x > 8\).
• Option D: Shows a line from -8 to 8, which is for \(|x| \leq 8\), incorrect.
• Option E: Shows the entire number line, which is not correct as \(|x| > 8\) excludes values between -8 and 8.
• Option F: Shows no shading, incorrect.

Answer:

The solution to \(|x|>8\) is \(x < - 8\) or \(x > 8\), and the correct graph is C. So the answer is C.