Solve the Equation: -|15| = Finding the Negative Absolute Value

Q: Why isn't the answer just 15?

The negative sign is outside the absolute value bars! This means we first find $ |15| = 15 $, then apply the negative to get $ -15 $.

Q: Can absolute values be negative?

Absolute values themselves are never negative - they're always zero or positive. But you can have a negative sign in front of an absolute value expression, like $ -|15| $.

Q: What's the difference between -|15| and |-15|?

$ -|15| = -15 $ (negative outside), but $ |-15| = 15 $ (negative inside). The position of the negative sign matters!

Q: How do I remember the order of operations here?

Think "inside first, outside second". First handle what's inside the absolute value bars, then apply anything outside (like the negative sign).

Q: Is this the same as -(15)?

Yes! $ -|15| = -(15) = -15 $. The absolute value of 15 is just 15, so putting a negative in front gives us negative fifteen.

Absolute Value with Negative Signs

$-\left|15\right| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-\left|15\right| =$

Step-by-step solution

To solve the given expression $-\left|15\right|$ , we need to find the absolute value of $15$ , then apply the negative sign.

The absolute value of a number is the non-negative value of that number without regard to its sign.

Thus, $\left|15\right| = 15$ .

Now apply the negative sign: $-\left|15\right| = -15$ .

Therefore, the answer is $-15$ .

Final Answer

$-15$

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value is always non-negative, but negative can apply outside
Technique: First find |15| = 15, then apply negative: -|15| = -15
Check: Verify absolute value gives 15, then negative makes it -15 ✓

Common Mistakes

Avoid these frequent errors

Thinking the negative sign changes the absolute value
Don't think -|15| equals |15| = 15! The negative is outside the absolute value bars, so it applies after finding |15|. Always find the absolute value first (which gives 15), then apply the negative sign to get -15.

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 answer just 15?

The negative sign is outside the absolute value bars! This means we first find $|15| = 15$ , then apply the negative to get $-15$ .

Can absolute values be negative?

Absolute values themselves are never negative - they're always zero or positive. But you can have a negative sign in front of an absolute value expression, like $-|15|$ .

What's the difference between -|15| and |-15|?

$-|15| = -15$ (negative outside), but $|-15| = 15$ (negative inside). The position of the negative sign matters!

How do I remember the order of operations here?

Think "inside first, outside second". First handle what's inside the absolute value bars, then apply anything outside (like the negative sign).

Is this the same as -(15)?

Yes! $-|15| = -(15) = -15$ . The absolute value of 15 is just 15, so putting a negative in front gives us negative fifteen.

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