ABSOLUTE VALUE

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Quick Summary

Absolute value represents distance from zero.
It is denoted by vertical bars: |x|.
The absolute value of a number is always non-negative.

\[ |x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases} \]

⚠️ Common Mistakes

Assuming absolute value always makes a number positive (e.g., |-x| = x is not always true).
Forgetting to consider both positive and negative cases when solving equations involving absolute value.
Incorrectly applying the definition when dealing with variables.

🌍 Real-World Uses

Calculating distances regardless of direction.
Error analysis in measurements.
Determining tolerances in engineering designs.

📝 Practice Problems

Problem 1: Evaluate |-5|.

Solution: The distance of -5 from zero is 5, so |-5| = 5.

Problem 2: Evaluate |3 - 7|.

Solution: |3 - 7| = |-4| = 4.

📋 Standards Alignment

CCSS.MATH.CONTENT.6.NS.C.7.C
CCSS.MATH.CONTENT.7.NS.A.1

🔗 Related Links

🍎 Teacher Insights

Use a number line to visually demonstrate the concept of distance from zero. Emphasize the importance of considering both positive and negative cases when solving absolute value equations.

🎓 Prerequisites

Integers
Number Line
Basic Arithmetic Operations

Check Your Knowledge

Q1: What is the absolute value of -8?

-8 0 8 16

Q2: Which of the following is equivalent to |x| = 5?

x = 5 only x = -5 only x = 5 or x = -5 x = 25

Frequently Asked Questions

Q: What is the absolute value of zero?
A: The absolute value of zero is zero, |0| = 0.

Q: Can an absolute value be negative?
A: No, the absolute value of a number is always non-negative.