A phrase describing a set of real numbers is given. Express the phrase as an inequality involving an absolute value.
All real numbers x at least 2 units from 3
  


The phrase "all real numbers \( x \) at least 2 units from 3" can be expressed as an absolute value inequality by interpreting the distance of \( x \) from 3 as:

\[
|x - 3| \geq 2
\]

This inequality states that the distance between \( x \) and 3 is at least 2 units.

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Here are 5 related questions to explore:
1. How would you express "all real numbers \( x \) less than 2 units from 5" as an inequality?
2. What is the solution set of the inequality \( |x - 4| \leq 3 \)?
3. How can you express "all real numbers within 3 units of 7" using absolute value?
4. What does the inequality \( |x - a| > b \) represent geometrically?
5. How do you solve absolute value inequalities like \( |x - 6| \geq 4 \)?

**Tip**: Absolute value inequalities are used to represent distances on the number line, often referring to "within" or "at least" certain distances from a point.

A phrase describing a set of real numbers is given. Express the phrase as an inequality involving an absolute value: All real numbers x at least 2 units from 3.

Learn how to express 'all real numbers x at least 2 units from 3' as an inequality using absolute value. This problem explores key algebra concepts such as absolute value and inequalities, suitable for Grades 7-9.

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