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

Question

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

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    0
    2021-09-09T15:18:34+00:00

    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

    0
    2021-09-09T15:18:55+00:00

    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

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