Solve the Absolute Value Expression: |5 - 3| Step by Step

Q: Why can't the answer be -2?

Absolute value always gives a non-negative result! The absolute value represents distance from zero, and distance is never negative. So $ |anything| \geq 0 $ always.

Q: What if I get a negative number inside the absolute value?

That's perfectly normal! If you had $ |3 - 5| = |-2| = 2 $, the absolute value removes the negative sign. Think of it as asking "how far from zero?"

Q: Do I always subtract from left to right?

Yes! Follow the order of operations. Calculate $ 5 - 3 $ exactly as written inside the bars first, then apply the absolute value to that result.

Q: How do I remember what absolute value means?

Think of absolute value as distance from zero on a number line. Whether you're at +2 or -2, you're still 2 units away from zero!

Q: Can I use a calculator for this?

Sure! But make sure you use parentheses: enter abs(5-3) or use the $ |x| $ button. Don't calculate 5, then 3, then try to subtract!

Absolute Value Operations with Simple Expressions

$|5 - 3| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|5 - 3| =$

Step-by-step solution

To solve the problem of finding the absolute value of $|5 - 3|$ , follow these steps:

Step 1: Evaluate the expression inside the absolute value, $5 - 3$ .
Step 2: Determine the result of this calculation.
Step 3: Apply the absolute value operation to the result obtained in Step 2.

Let's work through each step:

Step 1: Calculate $5 - 3$ . This gives us the result:

$5 - 3 = 2$

Step 2: Now apply the absolute value to this result:

$|2| = 2$

Therefore, the solution to the problem is $\boxed{2}$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Evaluate inside the absolute value bars first, then find distance
Technique: Calculate $5 - 3 = 2$ , then $|2| = 2$
Check: Absolute values are always non-negative, so $|5-3| = 2 \geq 0$ ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value of each number separately
Don't calculate $|5| - |3| = 5 - 3$ = wrong approach! This ignores order of operations and can give incorrect results for expressions like $|3 - 5|$ . Always evaluate what's inside the absolute value bars first, then apply the absolute value.

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 the answer be -2?

Absolute value always gives a non-negative result! The absolute value represents distance from zero, and distance is never negative. So $|anything| \geq 0$ always.

What if I get a negative number inside the absolute value?

That's perfectly normal! If you had $|3 - 5| = |-2| = 2$ , the absolute value removes the negative sign. Think of it as asking "how far from zero?"

Do I always subtract from left to right?

Yes! Follow the order of operations. Calculate $5 - 3$ exactly as written inside the bars first, then apply the absolute value to that result.

How do I remember what absolute value means?

Think of absolute value as distance from zero on a number line. Whether you're at +2 or -2, you're still 2 units away from zero!

Can I use a calculator for this?

Sure! But make sure you use parentheses: enter abs(5-3) or use the $|x|$ button. Don't calculate 5, then 3, then try to subtract!

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