Question
(a) \( |-5| \) (b) \( -(-5) \) (c) \( -|-5| \) (d) \( -|-(-5)| \)
Ask by Montgomery Coles. in Canada
Jan 17,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\begin{align*}
\text{(a)} &\quad |-5| = 5 \\
\text{(b)} &\quad -(-5) = 5 \\
\text{(c)} &\quad -|-5| = -5 \\
\text{(d)} &\quad -|-(-5)| = -5 \\
\end{align*}
\]
Solution
Let's evaluate each expression step by step:
### (a) \( |-5| \)
The absolute value of \(-5\) is the distance of \(-5\) from zero on the number line, which is:
\[
|-5| = 5
\]
### (b) \( -(-5) \)
Negating \(-5\) removes the negative sign:
\[
-(-5) = 5
\]
### (c) \( -|-5| \)
First, find the absolute value of \(-5\), which is \(5\), and then apply the negative sign:
\[
-|-5| = -5
\]
### (d) \( -|-(-5)| \)
Start by simplifying the innermost expression:
1. \( -(-5) = 5 \)
2. Then, take the absolute value: \( |5| = 5 \)
3. Finally, apply the negative sign:
\[
-|-(-5)| = -5
\]
### Summary of Results
\[
\begin{align*}
\text{(a)} &\quad |-5| = 5 \\
\text{(b)} &\quad -(-5) = 5 \\
\text{(c)} &\quad -|-5| = -5 \\
\text{(d)} &\quad -|-(-5)| = -5 \\
\end{align*}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The expression \( |-5| \) represents the absolute value of -5, which is 5. Absolute values disregard any negative sign, so whether you input -5 or 5, the output remains positive. Next, considering \( -(-5) \), you will find that this simplifies to 5. The double negative effectively cancels out, returning you to a positive result. This is the key reason why understanding signs in math can be quite liberating!
