Solve Absolute Value: |7 - 10| Step-by-Step Solution

Q: Why can't the absolute value be -3 if 7 - 10 = -3?

Absolute value measures distance, and distance is never negative! Think of it as asking "How far is -3 from 0 on a number line?" The answer is always 3 units.

Q: What does the absolute value symbol actually mean?

The vertical bars | | mean "distance from zero" or "make this number positive." So $ |x| $ is always ≥ 0.

Q: Do I always calculate what's inside the bars first?

Yes! Always solve the expression inside the absolute value bars first, then apply the absolute value rule. Work from the inside out.

Q: Can absolute value ever equal zero?

Yes! When the expression inside equals zero. For example, $ |5 - 5| = |0| = 0 $. Zero is the only number whose absolute value is itself.

Q: How do I remember that absolute value is always positive?

Think of it as distance! You can't walk a negative distance. Whether you go 3 steps left or right from zero, you still walked 3 steps total.

Absolute Value with Negative Results

$|7 - 10| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|7 - 10| =$

Step-by-step solution

The expression $|7 - 10|$ represents the absolute value of the difference between 7 and 10.

Calculate the difference: $7 - 10 = -3$ .

The absolute value of a negative number is its positive counterpart, so $|-3| = 3$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value always produces a non-negative result
Technique: Calculate inside first: $7 - 10 = -3$ , then $|-3| = 3$
Check: Distance from 0 on number line: -3 is 3 units away ✓

Common Mistakes

Avoid these frequent errors

Thinking absolute value can be negative
Don't assume |7 - 10| = -3 just because 7 - 10 = -3! Absolute value measures distance, which is always positive or zero. Always remember that |negative number| = positive number.

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 absolute value be -3 if 7 - 10 = -3?

Absolute value measures distance, and distance is never negative! Think of it as asking "How far is -3 from 0 on a number line?" The answer is always 3 units.

What does the absolute value symbol actually mean?

The vertical bars | | mean "distance from zero" or "make this number positive." So $|x|$ is always ≥ 0.

Do I always calculate what's inside the bars first?

Yes! Always solve the expression inside the absolute value bars first, then apply the absolute value rule. Work from the inside out.

Can absolute value ever equal zero?

Yes! When the expression inside equals zero. For example, $|5 - 5| = |0| = 0$ . Zero is the only number whose absolute value is itself.

How do I remember that absolute value is always positive?

Think of it as distance! You can't walk a negative distance. Whether you go 3 steps left or right from zero, you still walked 3 steps total.

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