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Given:
[tex]\[ Q = 7m + 3n, \quad R = 11 - 2m, \quad S = n + 5, \quad T = -m - 3n + 8 \][/tex]

Simplify [tex]\( R - [S + T] \)[/tex].

A. [tex]\(-3m - 4n + 14\)[/tex]
B. [tex]\(m - 2n - 2\)[/tex]
C. [tex]\(3m - 4n + 14\)[/tex]
D. [tex]\(-m + 2n - 2\)[/tex]

Sagot :

GinnyAnsweridn
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]
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