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2 years ago

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

Mathematics

2 answers:

antoniya [11.8K]2 years ago

8 0

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

strojnjashka [21]2 years ago

4 0

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

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