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

2 Answers
Mar 7, 2018

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

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