There is no absolute value function needed since the result is non-negative

Evaluate |3² - 7|: Absolute Value Expression Problem

Q: Why can't I just ignore the absolute value bars since the answer is positive?

You can't know the result is positive until you calculate what's inside first! The expression $ 3^2 - 7 $ could have been negative if the numbers were different. Always follow proper order of operations.

Q: What if the expression inside was negative instead?

If $ 3^2 - 7 $ gave us -2 instead of 2, then $ |-2| = 2 $. The absolute value always gives the positive version of any number.

Q: Do I need to show my work for each step?

Yes! Show: $ 3^2 = 9 $, then $ 9 - 7 = 2 $, then $ |2| = 2 $. This prevents mistakes and shows you understand the process.

Q: How do I remember the order of operations with absolute value?

Think of absolute value bars like parentheses - you must finish everything inside them first! Use PEMDAS: Parentheses (including absolute value), Exponents, Multiplication/Division, Addition/Subtraction.

Q: What's the difference between |3² - 7| and |3²| - |7|?

These are completely different! $ |3^2 - 7| = |2| = 2 $, but $ |3^2| - |7| = 9 - 7 = 2 $. The first applies absolute value to the entire expression, the second applies it to individual terms.

Q: Can absolute value ever equal a negative number?

Never! Absolute value measures distance from zero, which is always positive or zero. If you get a negative result, you made an error somewhere in your calculation.

Absolute Value with Order of Operations

$|3^2 - 7| =$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|3^2 - 7| =$

Step-by-step solution

The expression inside the absolute value is $3^2 - 7$ . Calculate $3^2$ :
$3^2 = 9$ .

Then, subtract $7$ from $9$ :
$9 - 7 = 2$ .

The absolute value of $2$ is $2$ , so the expression evaluates to $2$ . Therefore, $|3^2 - 7| = 2$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Order: Calculate inside absolute value bars first, then apply absolute value
Technique: Evaluate $3^2 = 9$ , then $9 - 7 = 2$
Check: Since 2 is positive, $|2| = 2$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Applying absolute value to individual terms first
Don't calculate |3²| - |7| = 9 - 7 = 2! This treats absolute value incorrectly by splitting it across terms. The result happens to be the same here, but this method fails for expressions like |2 - 5|. Always evaluate everything inside the absolute value bars first, then apply the absolute value to the final result.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

$\left|18\right|=$

FAQ

Everything you need to know about this question

Why can't I just ignore the absolute value bars since the answer is positive?

You can't know the result is positive until you calculate what's inside first! The expression $3^2 - 7$ could have been negative if the numbers were different. Always follow proper order of operations.

What if the expression inside was negative instead?

If $3^2 - 7$ gave us -2 instead of 2, then $|-2| = 2$ . The absolute value always gives the positive version of any number.

Do I need to show my work for each step?

Yes! Show: $3^2 = 9$ , then $9 - 7 = 2$ , then $|2| = 2$ . This prevents mistakes and shows you understand the process.

How do I remember the order of operations with absolute value?

Think of absolute value bars like parentheses - you must finish everything inside them first! Use PEMDAS: Parentheses (including absolute value), Exponents, Multiplication/Division, Addition/Subtraction.

What's the difference between |3² - 7| and |3²| - |7|?

These are completely different! $|3^2 - 7| = |2| = 2$ , but $|3^2| - |7| = 9 - 7 = 2$ . The first applies absolute value to the entire expression, the second applies it to individual terms.

Can absolute value ever equal a negative number?

Never! Absolute value measures distance from zero, which is always positive or zero. If you get a negative result, you made an error somewhere in your calculation.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Absolute Value and Inequality questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime