Calculate the Absolute Value: Finding |2 - 5|

Q: Why can't absolute value be negative?

Absolute value represents distance, and distance is never negative! Think of it as asking 'How far is this number from zero?' You can't be a negative distance away from something.

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

Yes! Always follow order of operations. Calculate $ 2 - 5 = -3 $ first, then find $ |-3| = 3 $.

Q: How do I remember which way the absolute value bars work?

Think of absolute value bars as 'make it positive' signs! Whatever you get inside, if it's negative, flip it to positive. If it's already positive, leave it alone.

Q: Can I get zero as an absolute value?

Absolutely! $ |0| = 0 $ because zero is exactly zero distance from itself. Zero is neither positive nor negative.

Absolute Value with Negative Results

Calculate the absolute value: $\left| 2 - 5 \right|$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the absolute value: $\left| 2 - 5 \right|$

Step-by-step solution

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

Step 1: Calculate the expression inside the absolute value.
Step 2: Determine the absolute value of the result.

Now, let's work through each step:
Step 1: Calculate $2 - 5$ .
$2 - 5 = -3$

Step 2: Determine the absolute value of $-3$ .
Since the number $-3$ is negative, the absolute value is calculated by changing its sign:
$\left| -3 \right| = 3$

Therefore, the absolute value of $2 - 5$ is $3$ .

The correct choice is: $3$ (Choice 1).

Final Answer

$3$

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: 2 - 5 = -3, then |−3| = 3
Check: Distance from -3 to 0 is 3 units on number line ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change negative results to positive
Don't leave |2 - 5| = -3 as your final answer! Absolute value bars mean distance, which is always positive or zero. Always make negative results positive: |-3| = 3.

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 never negative! Think of it as asking 'How far is this number from zero?' You can't be a negative distance away from something.

Do I calculate what's inside the absolute value bars first?

Yes! Always follow order of operations. Calculate $2 - 5 = -3$ first, then find $|-3| = 3$ .

What if the expression inside is already positive?

If the expression inside is positive or zero, the absolute value doesn't change it. For example, $|5 - 2| = |3| = 3$ .

How do I remember which way the absolute value bars work?

Think of absolute value bars as 'make it positive' signs! Whatever you get inside, if it's negative, flip it to positive. If it's already positive, leave it alone.

Can I get zero as an absolute value?

Absolutely! $|0| = 0$ because zero is exactly zero distance from itself. Zero is neither positive nor negative.

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