Simplify: −6(1/4 x - 2/3 x + 5/6 x) A) -2 1/2 x B) -x C) 2x D) 3/4 x

Mathematics

1 answer:

horrorfan [7]2 years ago

5 0

Answer:

(-5 x)/2

Step-by-step explanation:

Simplify the following:

-6 (x/4 - (2 x)/3 + (5 x)/6)

Put each term in x/4 - (2 x)/3 + (5 x)/6 over the common denominator 12: x/4 - (2 x)/3 + (5 x)/6 = (3 x)/12 - (8 x)/12 + (10 x)/12:

-6(3 x)/12 - (8 x)/12 + (10 x)/12

(3 x)/12 - (8 x)/12 + (10 x)/12 = (3 x - 8 x + 10 x)/12:

-6(3 x - 8 x + 10 x)/12

The gcd of -6 and 12 is 6, so (-6 (3 x - 8 x + 10 x))/12 = ((6 (-1)) (3 x - 8 x + 10 x))/(6×2) = 6/6×(-(3 x - 8 x + 10 x))/2 = (-(3 x - 8 x + 10 x))/2:

(-1 (3 x - 8 x + 10 x))/2

3 x - 8 x + 10 x = 5 x:

Answer: (-5 x)/2

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