Here is the detailed solution step-by-step, matching each expression with its simplified form:
1. Simplify the expression [tex]$-(-1)$[/tex]:
- The double negative turns positive.
- So, [tex]$-(-1) = 1$[/tex].
2. Simplify the expression [tex]$-|-1|$[/tex]:
- The absolute value of [tex]$-1$[/tex] is [tex]$1$[/tex].
- Adding a negative sign in front gives [tex]$-1$[/tex].
- So, [tex]$-|-1| = -1$[/tex].
3. Simplify the expression [tex]$-|1|$[/tex]:
- The absolute value of [tex]$1$[/tex] is [tex]$1$[/tex].
- Adding a negative sign in front gives [tex]$-1$[/tex].
- So, [tex]$-|1| = -1$[/tex].
4. Simplify the expression [tex]$|1|$[/tex]:
- The absolute value of [tex]$1$[/tex] is [tex]$1$[/tex].
- No additional operations are needed.
- So, [tex]$|1| = 1$[/tex].
5. Simplify the expression [tex]$|-1|$[/tex]:
- The absolute value of [tex]$-1$[/tex] is [tex]$1$[/tex].
- No additional operations are needed.
- So, [tex]$|-1| = 1$[/tex].
By matching each expression with its simplified form, we get:
\begin{tabular}{ll}
[tex]$-(-1)$[/tex] & 1 \\
[tex]$-|-1|$[/tex] & -1 \\
[tex]$-|1|$[/tex] & -1 \\
[tex]$|1|$[/tex] & 1 \\
[tex]$|-1|$[/tex] & 1 \\
\end{tabular}
