Question

Which of the following number line graphs shows the solution set of 3|x| + 1 > 7?

Answer 1

D

Explanation:

When doing this problem remember that absolute value is a number's distance from zero, and distance is always positive. So, absolute value makes any number positive. This means that |±x| = x. To find the correct number graph, first solve the inequality.

• 3|x| + 1 > 7

Subtract 1 from both sides

• 3|x| > 6

Divide both sides by 3

• |x| > 2

Then, we need to use absolute value. Any number with a distance from 0 greater than 2 fulfills this inequality. So, the number graph should represent -2 > x and x > 2. Additionally, because the inequality is looking for greater than but not equal to, the circles should be open.