Compare Absolute Values: |-25 + 5| vs |20| Equality Check

Q: Why do I need to calculate inside the absolute value bars first?

The order of operations requires you to do calculations inside grouping symbols (like absolute value bars) before applying the absolute value. Think of $ |-25 + 5| $ as $ |(-25 + 5)| $.

Q: What does absolute value actually do?

Absolute value gives you the distance from zero on a number line. Whether you start with a positive or negative number, absolute value always gives a non-negative result.

Q: How can a negative number have the same absolute value as a positive number?

Yes! $ |-20| = 20 $ and $ |20| = 20 $ because both numbers are the same distance from zero. The absolute value removes the negative sign.

Q: What if I got the wrong answer in the original question?

The explanation shows these expressions are equal, but the answer key says they're not equal. This appears to be an error in the answer key - your calculation showing they both equal 20 is correct!

Absolute Value Comparison with Negative Results

Are the expressions equal?

$\left|-25 + 5\right| \; \text{and} \; \left|20\right|$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Are the expressions equal?

$\left|-25 + 5\right| \; \text{and} \; \left|20\right|$

Step-by-step solution

First, let's evaluate both expressions separately.

Calculate $\left|-25 + 5\right|$ :

First, simplify inside the absolute value: $-25 + 5 = -20$ .
Now take the absolute value of $-20$ : $\left|-20\right| = 20$ because the absolute value of a negative number is its positive equivalent.

Now, calculate $\left|20\right|$ :

The number $20$ is already positive, so $\left|20\right| = 20$ .

Both expressions evaluate to $20$ , which means they are equal.

So, the correct answer to the problem is $\text{Yes}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value always gives non-negative results for any input
Technique: Calculate inside first: $-25 + 5 = -20$ , then $|-20| = 20$
Check: Both expressions equal 20, so they are equal ✓

Common Mistakes

Avoid these frequent errors

Comparing expressions without calculating them first
Don't assume $|-25 + 5|$ and $|20|$ are different just because they look different = wrong conclusion! The expressions might have the same value even if they appear different. Always calculate each expression completely before comparing.

Practice Quiz

Test your knowledge with interactive questions

$\left|-19\frac{1}{4}\right|=$

FAQ

Everything you need to know about this question

Why do I need to calculate inside the absolute value bars first?

The order of operations requires you to do calculations inside grouping symbols (like absolute value bars) before applying the absolute value. Think of $|-25 + 5|$ as $|(-25 + 5)|$ .

What does absolute value actually do?

Absolute value gives you the distance from zero on a number line. Whether you start with a positive or negative number, absolute value always gives a non-negative result.

How can a negative number have the same absolute value as a positive number?

Yes! $|-20| = 20$ and $|20| = 20$ because both numbers are the same distance from zero. The absolute value removes the negative sign.

Should I be surprised that these expressions are equal?

Not at all! Many different-looking expressions can have the same value. That's why we always calculate rather than just comparing how expressions look.

What if I got the wrong answer in the original question?

The explanation shows these expressions are equal, but the answer key says they're not equal. This appears to be an error in the answer key - your calculation showing they both equal 20 is correct!

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