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

Q: Why can't I just find the absolute value of each number separately?

Because the absolute value bars act like parentheses - you must complete all operations inside first! $ |-7 + 3| $ means find the absolute value of the result of -7 + 3, not the sum of individual absolute values.

Q: Can the absolute value ever be negative?

Never! The absolute value represents distance from zero, which is always positive or zero. If you get a negative answer, double-check your work.

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

Think of absolute value bars like parentheses in order of operations. Just like you'd solve (3 + 5) × 2 by doing 3 + 5 first, you solve $ |-7 + 3| $ by doing -7 + 3 first!

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

$ -4 $ is negative four (4 units left of zero), while $ |-4| = 4 $ is positive four (the distance from -4 to zero, which is 4 units).

Absolute Value with Negative Results

Evaluate the absolute value of the following expression:

$\left|-7 + 3\right|=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Evaluate the absolute value of the following expression:

$\left|-7 + 3\right|=$

Step-by-step solution

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

Simplify the expression inside the absolute value $-7 + 3$ .
Evaluate the absolute value of the resulting number.

Let’s perform the calculations:

First, simplify the expression $-7 + 3$ . This is equivalent to subtracting 3 from -7:

$-7 + 3 = -4$

Now, we find the absolute value of $-4$ :

The absolute value of a negative number is its positive equivalent. Therefore, $|-4| = 4$ .

Thus, the absolute value of $-7 + 3$ is $4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

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

Common Mistakes

Avoid these frequent errors

Finding absolute value before simplifying the expression
Don't evaluate |-7| + |3| = 7 + 3 = 10! This ignores the order of operations and treats each number separately. Always simplify inside the absolute value bars first: -7 + 3 = -4, then |-4| = 4.

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 find the absolute value of each number separately?

Because the absolute value bars act like parentheses - you must complete all operations inside first! $|-7 + 3|$ means find the absolute value of the result of -7 + 3, not the sum of individual absolute values.

What if the expression inside gives me a positive number?

Then the absolute value equals that positive number! For example, $|3 + 5| = |8| = 8$ . The absolute value of any positive number is just the number itself.

Can the absolute value ever be negative?

Never! The absolute value represents distance from zero, which is always positive or zero. If you get a negative answer, double-check your work.

How do I remember which operation to do first?

Think of absolute value bars like parentheses in order of operations. Just like you'd solve (3 + 5) × 2 by doing 3 + 5 first, you solve $|-7 + 3|$ by doing -7 + 3 first!

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

$-4$ is negative four (4 units left of zero), while $|-4| = 4$ is positive four (the distance from -4 to zero, which is 4 units).

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