Question

solve the inequality. graph the solutions. |x|>3 select the correct choice below and fill in any answer boxes in your choice. a. the solution is <x< (type integers or simplified fractions.) b. the solution is x= (type an integer or a simplified fraction.) c. the solution is x< or x> (type integers or simplified fractions.) d. the solution is all real numbers. e. there is no solution. choose the correct graph below. a. b. c. d. e. f. g. h.

Explanation:

Step1: Solve the absolute - value inequality

The absolute - value inequality \(|x|>a\) (\(a = 3\)) has the solution \(x<-a\) or \(x>a\) according to the property of absolute - value inequalities.
For \(|x|>3\), we get \(x < - 3\) or \(x>3\).

Answer:

C. The solution is \(x < - 3\) or \(x>3\).
The correct graph is C (since it has open circles at \(x=-3\) and \(x = 3\) and the shaded regions are to the left of \(x=-3\) and to the right of \(x = 3\)).