What would be equivalent to (-7 x + 8x + 19 y) - (6 y + 8 - 20 x - 16 y)

29y + 21x - 8

Would be equivalent to your expression

29 y + 21 x - 8

Step-by-step explanation:

Simplify the following:

-7 x + 8 x + 19 y - (6 y + 8 - 20 x - 16 y)

Grouping like terms, 6 y + 8 - 20 x - 16 y = (6 y - 16 y) - 20 x + 8:

-7 x + 8 x + 19 y - ((6 y - 16 y) - 20 x + 8)

6 y - 16 y = - 10 y:

-7 x + 8 x + 19 y - (-10 y - 20 x + 8)

Factor 2 out of - 10 y - 20 x + 8:

-7 x + 8 x + 19 y - 2 (-5 y - 10 x + 4)

Grouping like terms, - 7 x + 8 x + 19 y - 2 (-5 y - 10 x + 4) = 19 y - 2 (4 - 10 x - 5 y) + (8 x - 7 x):

19 y - 2 (4 - 10 x - 5 y) + (8 x - 7 x)

8 x - 7 x = x:

19 y - 2 (4 - 10 x - 5 y) + x

-2 (4 - 10 x - 5 y) = - 8 + 20 x + 10 y:

19 y + - 8 + 20 x + 10 y + x

Grouping like terms, 19 y - 8 + 20 x + 10 y + x = (19 y + 10 y) + (20 x + x) - 8:

(19 y + 10 y) + (20 x + x) - 8

19 y + 10 y = 29 y:

29 y + (20 x + x) - 8

20 x + x = 21 x:

Answer: 29 y + 21 x - 8