Question

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

Answer 1

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

Answer 2

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

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`