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Solving Absolute Value Equations

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Solving Absolute Value Equations

Study Guide

Key Definition

The absolute value of a number is its distance from zero on the number line. It is always non-negative. For example, $|-8| = 8$ and $|8| = 8$.

Important Notes

Absolute value is always non-negative: $|x| \geq 0$
Multiplicative property: $|x \times y| = |x| \times |y|$
Subadditivity property: $|x + y| \leq |x| + |y|$
Absolute value of zero: $|0| = 0$
Absolute value of a negative value: $|-x| = |x|$

Mathematical Notation

$|x|$ means the absolute value of $x$

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Absolute value measures distance from zero, which is why it is always positive or zero.

Remember

The absolute value of a number is its non-negative magnitude.

Quick Reference

Non-negativity:$|x| \geq 0$

Understanding Solving Absolute Value Equations

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The absolute value of a number is its distance from zero on the number line. This value is always positive or zero, for example, $|-3| = 3$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the solution to $|x| = 5$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If a teenager travels $|x|$ miles to school and $|x| = 3$, how far is the school from home?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Solve the equation $|2x - 4| = 6$.

Challenge Quiz

Single Choice Quiz

Advanced

Solve for $x$ in $|3x + 2| = 11$.

Recap

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Review key concepts and takeaways