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Subtraction of Algebraic Expression

Three times t...

Question

Three times the sum of $(5 x + 6 y) - {7 - (2 x - 4 y)}$ and ( $5 x - 6 y + 6$ ) is subtracted from ( $6 x - 8 y + 5$ ) is _____.

A

30 x - 4 y - 8

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B

15 x - 2 y - 4

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C

- 30 x + 4 y + 8

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D

- 15 x + 2 y + 4

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Solution

The correct option is C $- 30 x + 4 y + 8$
Three times the sum of $(5 x + 6 y) - {7 - (2 x - 4 y)}$ and ( $5 x - 6 y + 6)$ = $3 [(5 x + 6 y) - {7 - (2 x - 4 y)} + (5 x - 6 y + 6)]$
Simplifying the above expression,
$3 [(5 x + 6 y) - {7 - 2 x + 4 y} + (5 x - 6 y + 6)]$
= $3 (5 x + 6 y - 7 + 2 x - 4 y + 5 x - 6 y + 6$ )
= $3 (12 x - 4 y - 1)$
= $36 x - 12 y - 3$ ---------(1)

Subtracting expression (1) from ( $6 x - 8 y + 5)$ ,
= $(6 x - 8 y + 5) - (36 x - 12 y - 3)$
= $6 x - 8 y + 5 - 36 x + 12 y + 3$
= $- 30 x + 4 y + 8$

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