The inequality given is:

$|4x| \geq -2$

Let's break this down:

1. The absolute value of a number is always greater than or equal to 0.
2. Therefore, $|4x| \geq -2$ is always true because the absolute value of any expression is non-negative, and a non-negative number is always greater than or equal to -2.
3. Thus, there is no restriction on $x$. Every value of $x$ satisfies this inequality.

Hence, the solution is all real numbers, which is represented by the entire number line.

Now, let's examine the possible answers:

• The graph that shows the solution as all real numbers should have a shaded line extending from negative infinity to positive infinity.

Looking at the options:

• Option A appears to show a number line that represents all real numbers, which is the correct graph.

The interval notation for this solution would be $(-\infty, \infty)$.

Would you like more details or have any further questions about this? Here are some related questions to explore:

1. What is the difference between strict and non-strict inequalities?
2. How do you graph inequalities involving absolute values?
3. What is interval notation and how is it used to express solution sets?
4. What is the significance of solving inequalities in real-world contexts?
5. How do you solve inequalities involving absolute values with other types of expressions (e.g., linear terms)?

Tip: Always remember that absolute value inequalities with a negative right side (e.g., $|x| \geq -a$) will typically be true for all real numbers because absolute values cannot be negative.