We are tasked with choosing a value of $x$ that is at least 5 units away from 16. This problem deals with distance on the number line.

The distance between $x$ and 16 is represented by $|x - 16|$. For the distance to be at least 5 units, we need:

$|x - 16| \geq 5$

This inequality represents all values of $x$ that are at least 5 units away from 16.

Breaking it into two cases:

1. $x$ is 5 or more units greater than 16: $x - 16 \geq 5$ Solving for $x$: $x \geq 21$

2. $x$ is 5 or more units less than 16: $x - 16 \leq -5$ Solving for $x$: $x \leq 11$

Combined solution:

The values of $x$ that satisfy the inequality are:

$x \leq 11 \quad \text{or} \quad x \geq 21$

Final inequality:

$x \leq 11 \quad \text{or} \quad x \geq 21$ Alternatively, this can be written as: $x \in (-\infty, 11] \cup [21, \infty)$

Would you like further details or clarification?

Here are 5 related questions for practice:

1. What is the distance between $x = 11$ and $x = 16$?
2. Solve $|x - 7| \geq 3$.
3. Write an inequality representing values of $x$ less than 4 units away from 10.
4. How would the inequality change if we wanted $x$ at least 3 units away from 8?
5. What is the range of $x$ if $|x - 20| \leq 2$?

Tip: When dealing with absolute value inequalities, remember that $|A| \geq B$ means $A \geq B$ or $A \leq -B$.