Question

Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify [Q - R] + [S - T].

Answer 1

Answer: $[Q - R] + [S - T]=10m+7n-14$

Step-by-step explanation:

Given : $Q = 7m + 3n$,

$R = 11 -2m$,

$S = n + 5$, and

$T = -m - 3n + 8$

Now  , $Q-R= 7m + 3n-(11 - 2m)$

$Q-R= 7m +3n-11+2m$    [ ∵ (-)(+)=(-) and (-)(-)=(+)]

[Note : when -1 is outside the parenthesis it indicates that -1 should be multiplied with each of the terms present inside the parenthesis .]

$Q-R= 9m +3n-11$  [Combine like terms.]

$S-T=n + 5-(-m - 3n + 8)$

$S-T=n + 5+m+3n-8$    [ ∵ (-)(+)=(-) and (-)(-)=(+)]

$S-T=4n +m-3$    [Combine like terms.]

Now, $[Q - R] + [S - T]=[9m +3n-11]+[4n +m-3]$

$=9m +3n-11+4n+m-3$

$=10m+7n-14$  [combine like terms]

Hence, $[Q - R] + [S - T]=10m+7n-14$

Answer 2

Breaking each piece down
Q-R
(7m+3n) - (11- 2m)
7m + 3n -11- 2m
5m +3n - 11

S-T
(n+5)- (-m-3n)
n+5-m-3n
-2n +5 - m
 (5m +3n -11) + (-2n +5 -m )
= 4m + n -6