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Simplifying Absolute Value Expressions

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Simplifying Absolute Value Expressions

Study Guide

Key Definition

The absolute value of a number is its distance from 0 on the number line. It is always a positive number or zero, represented by $|a|$.

Important Notes

The absolute value of $|a|$ is always non-negative
For any positive number $a$, $|a| = a$
For any negative number $a$, $|a| = -a$
Absolute values ignore the sign of the number
Distance on the number line is always positive

Mathematical Notation

$|a|$ represents the absolute value of $a$

$+$ represents addition

$-$ represents subtraction

Remember to use proper notation when solving problems

Why It Works

Absolute value represents the magnitude of a number, shown as $|a|$, ensuring all values are non-negative.

Remember

For any real number a, $|-a| = |a|$.

Quick Reference

Property:$|a| \geq 0$ for any real number $a$

Understanding Simplifying Absolute Value Expressions

Choose your learning level

Beginner

Start here! Easy to understand

Beginner Explanation

Absolute value is the distance from zero. For any number $a$, $|a|$ is always positive or zero.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $|-7|$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Jenny's house is 7 miles east and Mark's is 7 miles west of the school. What is the total distance between their houses? Use |a| to find the answer.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the simplified form of $|x - 5|$ if $x = 3$.

Challenge Quiz

Single Choice Quiz

Advanced

What is the value of $|-4 + 2x|$ when $x = 3$?

Recap

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Review key concepts and takeaways