How do you solve #-101=-5(-5+8n)-6#?

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Answer 1 · 2017-05-19T17:54:47

See a solution process below:

First, add #color(red)(6)# to each side of the equation to isolate the term in parenthesis while keeping the equation balanced:

#-101 + color(red)(6) = -5(-5 + 8n) - 6 + color(red)(6)#

#-95 = -5(-5 + 8n) - 0#

#-95 = -5(-5 + 8n)#

Next, divide each side of the equation by #color(red)(-5)# to eliminate the need for the parenthesis while keeping the equation balanced:

#(-95)/color(red)(-5) = (-5(-5 + 8n))/color(red)(-5)#

#19 = (color(red)(cancel(color(black)(-5)))(-5 + 8n))/cancel(color(red)(-5))#

#19 = -5 + 8n#

Then, add #color(red)(5)# to each side of the equation to isolate the #n# term while keeping the equation balanced:

#color(red)(5) + 19 = color(red)(5) - 5 + 8n#

#24 = 0 + 8n#

#24 = 8n#

Now, divide each side of the equation by #color(red)(8)# to solve for #n# while keeping the equation balanced:

#24/color(red)(8) = (8n)/color(red)(8)#

#3 = (color(red)(cancel(color(black)(8)))n)/cancel(color(red)(8))#

#3 = n#

#n = 3#