Evaluate the Absolute Value Expression: |-7|

Q: Why isn't the absolute value of -7 equal to -7?

Because absolute value represents distance, and distance is never negative! Think of it this way: if you walk 7 steps in any direction from zero, you've traveled a distance of 7, not -7.

Q: What does the absolute value symbol | | actually mean?

The vertical bars | | tell you to find the distance from zero on the number line. It's like asking "how far away is this number from zero?"

Q: Is absolute value always positive?

Absolute value is always non-negative, meaning it's either positive or zero. The only number with absolute value of zero is zero itself: $ |0| = 0 $.

Q: How do I remember which direction to count on the number line?

You don't need to worry about direction! Count the units between your number and zero - it doesn't matter if you go left or right, the distance is the same.

Q: What about positive numbers like |5|?

For positive numbers, the absolute value stays the same: $ |5| = 5 $. The number is already 5 units away from zero in the positive direction.

Absolute Value with Negative Numbers

$\left|-7\right|=$

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Step-by-step written solution

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Understand the problem

$\left|-7\right|=$

Step-by-step solution

The absolute value of a number is its distance from zero on the number line, regardless of the direction. To find the absolute value of $-7$ , we need to look at the distance of $-7$ from zero, which is $7$ . Therefore, $\left|-7\right| = 7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value measures distance from zero on number line
Technique: Remove negative sign: $|-7| = 7$
Check: Count 7 units from zero in either direction on number line ✓

Common Mistakes

Avoid these frequent errors

Keeping the negative sign in the answer
Don't think $|-7| = -7$ ! This misses the key point that absolute value is always non-negative because it represents distance. Always remember that distance cannot be negative, so $|-7| = 7$ .

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 isn't the absolute value of -7 equal to -7?

Because absolute value represents distance, and distance is never negative! Think of it this way: if you walk 7 steps in any direction from zero, you've traveled a distance of 7, not -7.

What does the absolute value symbol | | actually mean?

The vertical bars | | tell you to find the distance from zero on the number line. It's like asking "how far away is this number from zero?"

Is absolute value always positive?

Absolute value is always non-negative, meaning it's either positive or zero. The only number with absolute value of zero is zero itself: $|0| = 0$ .

How do I remember which direction to count on the number line?

You don't need to worry about direction! Count the units between your number and zero - it doesn't matter if you go left or right, the distance is the same.

What about positive numbers like |5|?

For positive numbers, the absolute value stays the same: $|5| = 5$ . The number is already 5 units away from zero in the positive direction.

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