The statement says: "A quantity $x$ that is less than or equal to $-4$ or greater than or equal to 1." This is a compound inequality, and we need to translate it into a mathematical expression.

This statement breaks down into two parts:

1. $x \leq -4$
2. $x \geq 1$

The word "or" indicates that the solution is the union of these two conditions, meaning $x$ can satisfy either of the inequalities.

The compound inequality is:

$x \leq -4 \quad \text{or} \quad x \geq 1$

On a number line, this would be represented with a closed circle at $-4$ (indicating "less than or equal to") and shading to the left, and another closed circle at 1 (indicating "greater than or equal to") with shading to the right.

If you have multiple choices in your options (A, B, C, D, E), look for the graph that shows this pattern: two distinct regions, one from $-4$ to the left and the other from 1 to the right.

Do you need more details on how to interpret this graph or inequality?

Related Questions:

1. How do you graph compound inequalities with "and" instead of "or"?
2. What is the difference between open and closed circles on a number line graph?
3. How do compound inequalities relate to set notation?
4. Can you solve compound inequalities with different variables?
5. How would this inequality change if "greater than or equal to" became "greater than"?

Tip: When solving compound inequalities, pay close attention to whether the inequality uses "and" or "or" to decide how the solution set is combined.