Sure, I will match each expression on the left with its appropriate simplified form on the right, explaining each step along the way.
1. Simplifying [tex]\( (-5) \)[/tex]:
- When you have parentheses around a negative number, [tex]\( (-5) \)[/tex] simply evaluates to [tex]\(-5\)[/tex].
- Answer: [tex]\( (-5) = -5 \)[/tex].
2. Simplifying [tex]\( |-5| \)[/tex]:
- The absolute value of a number [tex]\( |-5| \)[/tex] is the distance from zero, regardless if it's positive or negative. Hence, [tex]\( |-5| = 5 \)[/tex].
- Answer: [tex]\( |-5| = 5 \)[/tex].
3. Simplifying [tex]\( |5| \)[/tex]:
- Similar to the previous absolute value, [tex]\( |5| \)[/tex] is the distance from zero, so [tex]\( |5| = 5 \)[/tex].
- Answer: [tex]\( |5| = 5 \)[/tex].
4. Simplifying [tex]\( -|5| \)[/tex]:
- First, calculate the absolute value inside. [tex]\( |5| = 5 \)[/tex].
- Then apply the negative sign outside, so [tex]\( -|5| = -5 \)[/tex].
- Answer: [tex]\( -|5| = -5 \)[/tex].
5. Simplifying [tex]\( -|-5| \)[/tex]:
- First, calculate the absolute value inside. [tex]\( |-5| = 5 \)[/tex].
- Then apply the negative sign outside, so [tex]\( -|-5| = -5 \)[/tex].
- Answer: [tex]\( -|-5| = -5 \)[/tex].
So, matching each expression with its simplified form:
[tex]\[
\begin{array}{ll}
(-5) & -5 \\
|-5| & 5 \\
|5| & 5 \\
-|5| & -5 \\
-|-5| & -5 \\
\end{array}
\][/tex]
