Suppose we want to choose a value of 
x
 at least 5 units away from 16.

Think about some values of 
x
 that meet this constraint.

Write an inequality that represents all values of 
x
 that meet this constraint.

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 \( A \leq -B \).

Suppose we want to choose a value of x at least 5 units away from 16. Think about some values of x that meet this constraint. Write an inequality that represents all values of x that meet this constraint.

Learn how to solve an absolute value inequality where x is at least 5 units away from 16. This step-by-step guide covers key algebraic concepts, including absolute value and inequalities, and is suitable for students in Grades 7-10.

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