Solve the Equation: Finding -|7| with Absolute Value

Q: What's the difference between -|7| and |-7|?

-|7| means the negative of the absolute value of 7, which is -7. But |-7| means the absolute value of negative 7, which is positive 7. The position of the negative sign matters!

Q: Why isn't the answer just 7?

The negative sign is outside the absolute value bars! You first find |7| = 7, then apply the negative sign to get -7. The absolute value doesn't "cancel out" the negative sign when it's outside.

Q: Is -|7| the same as (-1) × |7|?

Yes! -|7| is exactly the same as (-1) × |7|. Both equal -7 because you're multiplying the absolute value result by negative one.

Q: Can absolute values ever be negative?

No, absolute values are always non-negative (zero or positive). But when you put a negative sign in front of an absolute value, like -|7|, the final result becomes negative.

Q: How do I remember which comes first?

Think of absolute value bars like parentheses - you always do what's inside first! So for -|7|, first find |7| = 7, then apply the negative sign outside.

Absolute Value with Negative Signs

$-\left|7\right| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-\left|7\right| =$

Step-by-step solution

In the given expression, $-\left|7\right|$ , the absolute value of $7$ is required.

The absolute value, $\left|7\right|$ , is $7$ since absolute value denotes a non-negative distance from zero.

Applying the negative sign changes it to $-7$ .

The final result, therefore, is $-7$ .

Final Answer

$-7$

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value always gives non-negative distance from zero
Technique: First find |7| = 7, then apply negative sign: -(7) = -7
Check: Distance from 0 to 7 is 7, so -|7| = -7 ✓

Common Mistakes

Avoid these frequent errors

Confusing negative sign outside with sign inside absolute value
Don't think -|7| equals |−7| = 7! The negative sign is outside the absolute value, not inside. Always evaluate the absolute value first (|7| = 7), then apply the negative sign (-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

What's the difference between -|7| and |-7|?

-|7| means the negative of the absolute value of 7, which is -7. But |-7| means the absolute value of negative 7, which is positive 7. The position of the negative sign matters!

Why isn't the answer just 7?

The negative sign is outside the absolute value bars! You first find |7| = 7, then apply the negative sign to get -7. The absolute value doesn't "cancel out" the negative sign when it's outside.

Is -|7| the same as (-1) × |7|?

Yes! -|7| is exactly the same as (-1) × |7|. Both equal -7 because you're multiplying the absolute value result by negative one.

Can absolute values ever be negative?

No, absolute values are always non-negative (zero or positive). But when you put a negative sign in front of an absolute value, like -|7|, the final result becomes negative.

How do I remember which comes first?

Think of absolute value bars like parentheses - you always do what's inside first! So for -|7|, first find |7| = 7, then apply the negative sign outside.

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