Absolute Value Equations Worksheet with Answer Key

📚 Topic Summary

Absolute value equations involve finding the values of a variable that make the expression inside the absolute value symbols equal to a specific number. Remember, the absolute value of a number is its distance from zero, so it's always non-negative. For example, $|x| = 5$ means $x$ could be 5 or -5 because both are 5 units away from zero.

To solve absolute value equations, you typically need to consider two cases: one where the expression inside the absolute value is positive or zero, and another where it's negative. This leads to two separate equations that you solve independently. Let's dive into some practice!

🧠 Part A: Vocabulary

Match each term with its definition:

✏️ Part B: Fill in the Blanks

Complete the following paragraph using the words: positive, negative, distance, zero, equation.

The absolute value of a number represents its ______ from ______. When solving an absolute value ______, we consider both the ______ and ______ possibilities of the expression inside the absolute value.

🤔 Part C: Critical Thinking

Explain why absolute value equations can have two solutions. Use an example to illustrate your explanation.

🔑 Answer Key

Part A: Vocabulary

• 🔍 1. Absolute Value - B. The distance of a number from zero.
• 💡 2. Equation - A. A statement that two expressions are equal.
• 📝 3. Variable - D. A symbol (usually a letter) that represents a number.
• ➗ 4. Solution - C. A value that, when substituted for a variable, makes the equation true.
• ➕ 5. Expression - E. A combination of numbers, variables, and operations.

Part B: Fill in the Blanks

The absolute value of a number represents its distance from zero. When solving an absolute value equation, we consider both the positive and negative possibilities of the expression inside the absolute value.

Part C: Critical Thinking

Absolute value equations can have two solutions because the absolute value of a number is its distance from zero. For example, in the equation $|x| = 3$, both $x = 3$ and $x = -3$ are solutions because both 3 and -3 are 3 units away from zero.