Question

12 multiple choice 1 point which of the following is the graph of |x| > 3? 13 multiple choice 1 point solve: 15 > -5x > -5

Explanation:

Step1: Solve the absolute - value inequality \(|x|>3\)

The absolute - value inequality \(|x|>a\) (\(a > 0\)) is equivalent to \(x > a\) or \(x<-a\). So, \(|x|>3\) is equivalent to \(x > 3\) or \(x<-3\). On a number line, this is represented by an open - circle at \(x = 3\) and an arrow pointing to the right, and an open - circle at \(x=-3\) and an arrow pointing to the left.

Step2: Solve the compound inequality \(15>-5x > - 5\)

Divide each part of the compound inequality by \(-5\). When dividing an inequality by a negative number, the direction of the inequality signs changes. So, \(\frac{15}{-5}<\frac{-5x}{-5}<\frac{-5}{-5}\), which simplifies to \(-3 < x<1\).

Answer:

1. The graph with open - circles at \(x = 3\) and \(x=-3\) and arrows pointing away from these points (the second graph among the given options for question 12).
2. \( - 3x>-3\) (the fourth option for question 13).