Evaluate the Absolute Value Expression: |-7 + 3|

Q: Why can't I just make both numbers positive first?

Because the absolute value bars act like parentheses! You must follow the order of operations and evaluate what's inside first. $ |-7 + 3| $ means "the absolute value of the sum," not "the sum of the absolute values."

Q: What if the result inside is already positive?

Then the absolute value doesn't change it! For example, $ |2 + 3| = |5| = 5 $. The absolute value of a positive number is just that same positive number.

Q: How do I remember which operation to do first?

Think of absolute value bars like parentheses in PEMDAS! Just like you evaluate $ 2(3 + 4) $ by doing $ 3 + 4 $ first, you evaluate what's inside the absolute value bars first.

Q: Can an absolute value ever be negative?

Never! The absolute value represents distance from zero on a number line, and distance is always positive or zero. So $ |anything| ≥ 0 $ always.

Q: What's the difference between -4 and |-4|?

$ -4 $ is negative four, while $ |-4| = 4 $ is positive four. The absolute value removes the negative sign, giving you the positive distance from zero.

Absolute Value with Negative Results

$|-7 + 3| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|-7 + 3| =$

Step-by-step solution

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

Step 1: Evaluate the expression inside the absolute value.
Step 2: Apply the absolute value calculation based on the result from Step 1.

Now, let's work through each step in detail:

Step 1: We evaluate the expression inside the absolute value: $-7 + 3$ .

Calculating this gives us:

$-7 + 3 = -4$

Step 2: Apply the absolute value.

The absolute value of any number, $-a$ , is its positive counterpart. Therefore, we calculate:

$|-4| = 4$

Conclusion: The absolute value of $-7 + 3$ is $4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: Always evaluate inside the absolute value bars first
Technique: Calculate -7 + 3 = -4, then find |-4| = 4
Check: The result is always positive or zero: |any number| ≥ 0 ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value before evaluating inside
Don't find |-7| + |3| = 7 + 3 = 10! This ignores order of operations and gives the wrong answer. 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 I just make both numbers positive first?

Because the absolute value bars act like parentheses! You must follow the order of operations and evaluate what's inside first. $|-7 + 3|$ means "the absolute value of the sum," not "the sum of the absolute values."

What if the result inside is already positive?

Then the absolute value doesn't change it! For example, $|2 + 3| = |5| = 5$ . The absolute value of a positive number is just that same positive number.

How do I remember which operation to do first?

Think of absolute value bars like parentheses in PEMDAS! Just like you evaluate $2(3 + 4)$ by doing $3 + 4$ first, you evaluate what's inside the absolute value bars first.

Can an absolute value ever be negative?

Never! The absolute value represents distance from zero on a number line, and distance is always positive or zero. So $|anything| ≥ 0$ always.

What's the difference between -4 and |-4|?

$-4$ is negative four, while $|-4| = 4$ is positive four. The absolute value removes the negative sign, giving you the positive distance from zero.

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