How do you solve #-232= 6( - 7n + 3) - 8n#?

2 Answers
Mar 7, 2018

Answer:

See a solution process below:

Explanation:

First, expand the terms in the parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Then group and combine common terms:

#-232 = color(red)(6)(-7n + 3) - 8n#

#-232 = (color(red)(6) xx -7n) + (color(red)(6) xx 3) - 8n#

#-232 = -42n + 18 - 8n#

#-232 = -42n - 8n + 18#

#-232 = (-42 - 8)n + 18#

#-232 = -50n + 18#

Next, subtract #color(red)(18)# from each side of the equation to isolate the #n# term while keeping the equation balanced:

#-232 - color(red)(18) = -50n + 18 - color(red)(18)#

#-250 = -50n + 0#

#-250 = -50n#

Now, divide each side of the equation by #color(red)(-50)# to solve for #n# while keeping the equation balanced:

#(-250)/color(red)(-50) = (-50n)/color(red)(-50)#

#5 = (color(red)(cancel(color(black)(-50)))n)/cancel(color(red)(-50))#

#5 = n#

#n = 5#

Mar 7, 2018

Answer:

#n = 5#

Explanation:

#−232=6 ("-"7n+3)−8n#      Solve for #n#

1) Clear the parentheses by distributing the #6#
After you have multiplied both of the terms inside the parentheses by 6, you will have this:
#- 232 = - 42 n + 18 - 8n#

2) Combine like terms
After you combine #-42 n# with #-8n#, you will get this
#-232 = -50 n + 18#

3) Subtract #18# from both sides to isolate the #-50  n# term
#-250 = - 50 n#

4) Divide both sides by #- 50# to isolate #n#
#5 = n#

Answer:
#n = 5#

#color(white)(mmmmmm)# ――――――――

Check

Sub in #5# in the place of #n# in the original equation

#−232=6 ("-"7 n  +3)−8 n#
#−232=6 ("-"7(5)+3)−8(5)#

1) Multiply   #"-"7(5)#  inside the parentheses
#−232=6 (-35+3)−8(5)#

2) Combine #-35# with #3# inside the parentheses
#−232=6  (-32)−8(5)#

3) Clear the parentheses by distributing the #6# and the #8#
#-232  = -192 - 40#

4) Combine like terms
#-232  = -232#

#Check#