Evaluate the Absolute Value Expression: |-8 + 3|

Q: Why can't I just make everything positive right away?

The absolute value bars act like parentheses - you must follow order of operations! Calculate inside the bars first: -8 + 3 = -5, then apply absolute value: |-5| = 5.

Q: What if the expression inside is already positive?

If the result inside the absolute value bars is positive, the absolute value doesn't change it. For example: $ |3 + 2| = |5| = 5 $.

Q: How do I remember when to use the negative sign?

Never use a negative sign with absolute value results! The absolute value of any number is always positive or zero. Think of it as distance from zero.

Q: What's the difference between |-8| + |3| and |-8 + 3|?

The first expression: |-8| + |3| = 8 + 3 = 11. The second: |-8 + 3| = |-5| = 5. Order of operations matters! Parentheses (or absolute value bars) come first.

Q: Can absolute value ever equal a negative number?

No, never! Absolute value represents distance, which is always positive or zero. If you get a negative answer, check your work - you made an error somewhere.

Absolute Value with Negative Expressions

$|-8 + 3| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|-8 + 3| =$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Simplify the expression inside the absolute value symbol.
Step 2: Apply the definition of absolute value to the simplified expression.

Step 1: We start by evaluating the expression inside the absolute value, $-8 + 3$ .
When we calculate $-8 + 3$ , we perform the operation:

$-8 + 3 = -5$ .

Step 2: Now that we have simplified the expression to $-5$ , we apply the absolute value definition. The absolute value of $-5$ is found using the rule for absolute values:

Since $-5$ is less than zero, we use the definition: $|x| = -x$ when $x < 0$ .

Therefore, $|-5| = -(-5) = 5$ .

Thus, the solution to the problem is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: Always calculate inside the absolute value bars first
Technique: For $|-8 + 3|$ , compute -8 + 3 = -5 first
Check: Since |-5| = 5, verify that 5 is positive ✓

Common Mistakes

Avoid these frequent errors

Applying absolute value to each term separately
Don't split |-8 + 3| into |−8| + |3| = 8 + 3 = 11! This ignores order of operations and gives the wrong answer. Always simplify the expression inside the absolute value bars first, then apply the absolute value to the result.

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 I just make everything positive right away?

The absolute value bars act like parentheses - you must follow order of operations! Calculate inside the bars first: -8 + 3 = -5, then apply absolute value: |-5| = 5.

What if the expression inside is already positive?

If the result inside the absolute value bars is positive, the absolute value doesn't change it. For example: $|3 + 2| = |5| = 5$ .

How do I remember when to use the negative sign?

Never use a negative sign with absolute value results! The absolute value of any number is always positive or zero. Think of it as distance from zero.

What's the difference between |-8| + |3| and |-8 + 3|?

The first expression: |-8| + |3| = 8 + 3 = 11. The second: |-8 + 3| = |-5| = 5. Order of operations matters! Parentheses (or absolute value bars) come first.

Can absolute value ever equal a negative number?

No, never! Absolute value represents distance, which is always positive or zero. If you get a negative answer, check your work - you made an error somewhere.

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