Solve: Finding the Opposite of Absolute Value -|-18|

Q: Why isn't the answer just 18 since absolute value makes things positive?

Great question! The absolute value $ |-18| $ does equal 18, but there's a negative sign outside the absolute value bars. So we get $ -18 $ as our final answer.

Q: What's the difference between |-18| and -|-18|?

$ |-18| = 18 $ (just absolute value), but $ -|-18| = -18 $ (absolute value then apply the negative). The placement of the negative sign matters!

Q: Does the negative inside the absolute value bars matter?

No! Absolute value always gives the positive distance from zero. So $ |-18| = |18| = 18 $. The sign inside doesn't affect the absolute value result.

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

Think of it as two separate steps: First, find the absolute value (which gives 18), then apply any operations outside the bars (the negative sign gives us -18).

Q: Can absolute value ever give a negative answer?

Never! Absolute value by itself always gives a positive result or zero. Only operations outside the absolute value bars (like our negative sign) can make the final answer negative.

Absolute Value with Negative Sign Operations

$−\left|-18\right|=$

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Step-by-step written solution

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Understand the problem

$−\left|-18\right|=$

Step-by-step solution

The problem requires us to evaluate the expression $-\left|-18\right|$ .

Step 1: Calculate the absolute value of $-18$ .

The absolute value of a number is the positive version of the number if it's negative. Therefore:
$\left|-18\right| = 18$

Step 2: Apply the negative sign to the result of the absolute value operation.

We attach the negative sign that is outside the absolute value:
$-\left|-18\right| = -18$

Therefore, the result of the expression $-\left|-18\right|$ is $-18$ .

Final Answer

$-18$

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value always gives a positive result first
Technique: Calculate $|-18| = 18$ , then apply negative sign
Check: Final result $-|-18| = -18$ should be negative ✓

Common Mistakes

Avoid these frequent errors

Confusing negative sign placement
Don't think $-|-18| = 18$ because there's a negative inside! The negative sign outside the absolute value bars applies AFTER you find the absolute value. Always calculate the absolute value first (getting 18), then apply the outside negative sign to get -18.

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 18 since absolute value makes things positive?

Great question! The absolute value $|-18|$ does equal 18, but there's a negative sign outside the absolute value bars. So we get $-18$ as our final answer.

What's the difference between |-18| and -|-18|?

$|-18| = 18$ (just absolute value), but $-|-18| = -18$ (absolute value then apply the negative). The placement of the negative sign matters!

Does the negative inside the absolute value bars matter?

No! Absolute value always gives the positive distance from zero. So $|-18| = |18| = 18$ . The sign inside doesn't affect the absolute value result.

How do I remember the order of operations here?

Think of it as two separate steps: First, find the absolute value (which gives 18), then apply any operations outside the bars (the negative sign gives us -18).

Can absolute value ever give a negative answer?

Never! Absolute value by itself always gives a positive result or zero. Only operations outside the absolute value bars (like our negative sign) can make the final answer negative.

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