Question

On a number line, illustrate all the points whose coordinates satisfy the inequality |x + 3| < 4. Provide the representation on the number line.

Answer 1

The graph of the solution set of |x + 3| < 4 is in the image at the end.

How to graph the inequality?

We want to graph the absolute value inequality:

|x + 3| < 4

To do so, we should start by solving it. If we break the absolute value part we will get:

x + 3 < 4

x + 3 > -4

Solving these two we will get:

x < 4 - 3 = 1

x > -4 - 3 = -7

Then we have:

x > -7 or x < 1, this gives:

-7 < x < 1

We need to graph a segment that goes from -7 to 1, and that does not include these two numbers.