Solve Absolute Value Expression: |5 - 9| Calculation

Q: Why isn't the answer -4 if 5 - 9 = -4?

Great question! The absolute value bars change everything. While $ 5 - 9 = -4 $, the absolute value $ |5 - 9| = |-4| = 4 $. Think of it as distance - you can't have negative distance!

Q: What does absolute value actually mean?

Absolute value means the distance from zero on a number line. Since distance is always positive, absolute value is always positive (or zero). For example, both 4 and -4 are 4 units away from zero.

Q: Do I always calculate what's inside the bars first?

Yes! Always solve inside the absolute value bars first, just like parentheses in order of operations. Then apply the absolute value to make the result non-negative.

Q: Can absolute value ever be negative?

Never! Absolute value is always zero or positive. If you get a negative answer, check your work. The absolute value represents distance, and distance cannot be negative.

Q: What if there's nothing to calculate inside the bars?

If you see something like $ |7| $, the answer is just 7. For $ |-3| $, the answer is 3. You only need to make negative numbers positive!

Absolute Value with Negative Results

$|5 - 9| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|5 - 9| =$

Step-by-step solution

To solve this problem, we will follow these steps:

Evaluate the arithmetic expression inside the absolute value symbol.
Apply the definition of absolute value to determine the result.

Now, let's work through each step:
Step 1: Evaluate the expression $5 - 9$ .
- To find $5 - 9$ , we subtract 9 from 5, which gives us $-4$ .

Step 2: Apply the absolute value.
- The absolute value of a number is its non-negative value. Since $-4$ is negative, we take the opposite: $|-4| = 4$ .

Therefore, the absolute value of $5 - 9$ is $4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value gives the distance from zero on number line
Technique: First calculate inside: 5 - 9 = -4, then apply |−4| = 4
Check: Distance from -4 to 0 is 4 units on number line ✓

Common Mistakes

Avoid these frequent errors

Confusing absolute value with the original negative result
Don't think |5 - 9| = -4 because that's what's inside the bars! The absolute value symbol means you must make the result positive. Always remember that |negative number| = positive number.

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 isn't the answer -4 if 5 - 9 = -4?

Great question! The absolute value bars change everything. While $5 - 9 = -4$ , the absolute value $|5 - 9| = |-4| = 4$ . Think of it as distance - you can't have negative distance!

What does absolute value actually mean?

Absolute value means the distance from zero on a number line. Since distance is always positive, absolute value is always positive (or zero). For example, both 4 and -4 are 4 units away from zero.

Do I always calculate what's inside the bars first?

Yes! Always solve inside the absolute value bars first, just like parentheses in order of operations. Then apply the absolute value to make the result non-negative.

Can absolute value ever be negative?

Never! Absolute value is always zero or positive. If you get a negative answer, check your work. The absolute value represents distance, and distance cannot be negative.

What if there's nothing to calculate inside the bars?

If you see something like $|7|$ , the answer is just 7. For $|-3|$ , the answer is 3. You only need to make negative numbers positive!

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