Calculate |5 - 7|: Solving an Absolute Value Expression

Q: Why can't the absolute value be negative?

Absolute value represents distance, and distance is never negative! Think of it as "how far from zero?" - whether you're at -2 or +2, you're still 2 units away from zero.

Q: Do I always subtract first before applying absolute value?

Yes! Always calculate what's inside the absolute value bars first. In $ |5 - 7| $, do $ 5 - 7 = -2 $, then find $ |-2| = 2 $.

Q: How do I remember which number to subtract from which?

Follow the order exactly as written! In $ |5 - 7| $, subtract 7 from 5, not the other way around. The absolute value will fix any negative result.

Q: Is there a shortcut for absolute value problems?

You can think of it as "the positive distance between two numbers." For $ |5 - 7| $, it's the distance between 5 and 7 on a number line, which is always 2!

Absolute Value with Negative Results

$|5 - 7| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|5 - 7| =$

Step-by-step solution

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

Step 1: Subtract 7 from 5 to find $5 - 7$ .
Step 2: Determine the sign of the result from Step 1.
Step 3: Apply the absolute value definition to the result.

Now, let's work through each step:

Step 1: Calculate $5 - 7$ .
$5 - 7 = -2$

Step 2: The result from Step 1, $-2$ , is negative.

Step 3: Apply the absolute value definition. Since the result is negative, we take the opposite of $-2$ :
$|-2| = 2$

Therefore, the solution to the problem is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value gives the distance from zero on number line
Technique: Calculate inside first: $5 - 7 = -2$ , then apply absolute value
Check: Distance from 0 to -2 is 2 units, so $|-2| = 2$ ✓

Common Mistakes

Avoid these frequent errors

Keeping the negative sign in final answer
Don't write $|5 - 7| = -2$ ! Absolute value always gives a non-negative result because it measures distance. Always make the final answer positive when the expression inside is negative.

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 negative?

Absolute value represents distance, and distance is never negative! Think of it as "how far from zero?" - whether you're at -2 or +2, you're still 2 units away from zero.

Do I always subtract first before applying absolute value?

Yes! Always calculate what's inside the absolute value bars first. In $|5 - 7|$ , do $5 - 7 = -2$ , then find $|-2| = 2$ .

What if the result inside is already positive?

Perfect! If the expression inside gives a positive number, the absolute value stays the same. For example: $|7 - 5| = |2| = 2$ .

How do I remember which number to subtract from which?

Follow the order exactly as written! In $|5 - 7|$ , subtract 7 from 5, not the other way around. The absolute value will fix any negative result.

Is there a shortcut for absolute value problems?

You can think of it as "the positive distance between two numbers." For $|5 - 7|$ , it's the distance between 5 and 7 on a number line, which is always 2!

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