To simplify [tex]\( R - [S + T] \)[/tex], we start by breaking down the problem step-by-step.
Firstly, we need to find the expression for [tex]\( S + T \)[/tex]:
Given:
[tex]\[ S = n + 5 \][/tex]
[tex]\[ T = -m - 3n + 8 \][/tex]
Combine [tex]\( S \)[/tex] and [tex]\( T \)[/tex]:
[tex]\[
S + T = (n + 5) + (-m - 3n + 8)
\][/tex]
Next, simplify the terms:
[tex]\[
S + T = n + 5 - m - 3n + 8
\][/tex]
Combine like terms:
[tex]\[
S + T = -m - 2n + 13
\][/tex]
Now we need to compute [tex]\( R - [S + T] \)[/tex]:
Given [tex]\( R = 11 - 2m \)[/tex], we have:
[tex]\[
R - [S + T] = (11 - 2m) - (-m - 2n + 13)
\][/tex]
Distribute the negative sign:
[tex]\[
R - [S + T] = 11 - 2m + m + 2n - 13
\][/tex]
Combine like terms:
[tex]\[
R - [S + T] = -m + 2n + (11 - 13)
\][/tex]
[tex]\[
R - [S + T] = -m + 2n - 2
\][/tex]
Thus, [tex]\( R - [S + T] \)[/tex] simplifies to:
[tex]\[
-m + 2n - 2
\][/tex]
The correct answer is:
[tex]\[
-m + 2n - 2
\][/tex]
