To simplify the expression [tex]\(R - S + T\)[/tex] given the values of [tex]\(R\)[/tex], [tex]\(S\)[/tex], and [tex]\(T\)[/tex], let's follow a step-by-step approach:
Given:
[tex]\[ R = 11 - 2m \][/tex]
[tex]\[ S = n + 5 \][/tex]
[tex]\[ T = -m - 3n + 8 \][/tex]
We want to simplify:
[tex]\[ R - S + T \][/tex]
First, substitute the given expressions into [tex]\(R - S + T\)[/tex]:
[tex]\[ R - S + T = (11 - 2m) - (n + 5) + (-m - 3n + 8) \][/tex]
Now, distribute the minus sign through the expression in parentheses for [tex]\(S\)[/tex]:
[tex]\[ = 11 - 2m - n - 5 + (-m - 3n + 8) \][/tex]
Next, combine all the terms:
[tex]\[ = 11 - 5 + 8 - 2m - m - n - 3n \][/tex]
Let's group similar terms together:
[tex]\[ = (11 - 5 + 8) + (-2m - m) + (-n - 3n) \][/tex]
Simplify each group individually:
[tex]\[ = 14 - 3m - 4n \][/tex]
So, the simplified form of the expression [tex]\( R - S + T \)[/tex] is:
[tex]\[ = -3m - 4n + 14 \][/tex]
Thus, the simplified expression is:
[tex]\[ \boxed{-3m - 4n + 14} \][/tex]
