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]3 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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Ally and Beck went fishing and caught a total of 75 fish. At home,

tigry1 [53]

Answer:

Beck actually caught 45 fish

Step-by-step explanation:

System of Equations

We call the following variables:

x = number of fish Ally caught

y = number of fish Beck caught

They caught a total of 75 fish, thus:

x + y = 75 [1]

If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:

3y = 2x + 75 [2]

From [1]:

x = 75 - y [3]

Substituting in [2]:

3y = 2(75 - y) + 75

Operating:

3y = 150 - 2y + 75

Simplifying:

5y = 225

Dividing by 5:

y = 45

Beck actually caught 45 fish