Calculate the Absolute Value: Evaluating |2 - 7|

Q: Why can't absolute value be negative?

Absolute value represents distance, and distance is always positive! Think of it as "how far is this number from zero?" Since you can't have negative distance, absolute value is never negative.

Q: Do I always subtract left to right inside absolute value?

Yes! Always follow the order exactly as written. $ |2 - 7| $ means calculate $ 2 - 7 = -5 $ first, then take the absolute value to get 5.

Q: How do I remember what absolute value does?

Think of absolute value as "removing the negative sign" or asking "how far from zero?" Both ways help you remember that the answer is always non-negative!

Q: What's the difference between -|5| and |-5|?

$ |-5| = 5 $ (absolute value first, so positive), but $ -|5| = -5 $ (absolute value of 5 is 5, then apply the negative sign). Order of operations matters!

Absolute Value with Negative Results

$|2 - 7| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|2 - 7| =$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Compute the result of $2 - 7$ .
Step 2: Apply the definition of absolute value to the result obtained.

Let's work through each step:
Step 1: Calculate $2 - 7$ .
This results in $2 - 7 = -5$ .

Step 2: Take the absolute value of $-5$ .
The absolute value $|-5|$ is equal to $5$ . Absolute value represents the distance of a number from zero on the number line, making it always non-negative.

Therefore, the solution to the problem is $\boxed{5}$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value makes any number non-negative by removing sign
Technique: First calculate $2 - 7 = -5$ , then $|-5| = 5$
Check: Distance from zero on number line: -5 is 5 units away ✓

Common Mistakes

Avoid these frequent errors

Forgetting to remove the negative sign
Don't leave the negative sign in your final answer like $|-5| = -5$ ! This completely misses what absolute value means - it's the distance from zero, which is always positive. Always make your final answer positive (or zero).

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 absolute value be negative?

Absolute value represents distance, and distance is always positive! Think of it as "how far is this number from zero?" Since you can't have negative distance, absolute value is never negative.

What if the number inside is already positive?

If the number inside the absolute value bars is already positive, like $|3|$ , then the answer stays the same: $|3| = 3$ . Absolute value only changes negative numbers!

Do I always subtract left to right inside absolute value?

Yes! Always follow the order exactly as written. $|2 - 7|$ means calculate $2 - 7 = -5$ first, then take the absolute value to get 5.

How do I remember what absolute value does?

Think of absolute value as "removing the negative sign" or asking "how far from zero?" Both ways help you remember that the answer is always non-negative!

What's the difference between -|5| and |-5|?

$|-5| = 5$ (absolute value first, so positive), but $-|5| = -5$ (absolute value of 5 is 5, then apply the negative sign). Order of operations matters!

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