Question

Given the inequality: 3 |x + 1| < 12
Part III: Explain what the graph of the solutions for the equation would look like.

Be sure to include the following:

the types of endpoints (open and/or closed)
the endpoint numbers
direction of shading
(For example: The graph would have an open circle at 4, shaded to the right, and a closed circle at 9, shaded to the left.)
A number line includes these numbers: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6

Answer 1

Solve: 3|x + 1| < 12 ⇒ |x + 1| < 4 ⇒ -4 < x + 1 < 4 ⇒ -5 < x < 3.

So on the given number line:
- Open circle at -5 (not included).
- Open circle at 3 (not included).
- Shade the region between -5 and 3 (i.e., to the right of -5 and to the left of 3).