How do you solve -6n-10=-2n+4(1-3n)?

2 Answers
Mar 30, 2017

n=1.75

Explanation:

This might look a little intimidating, but the process is fairly straightforward.
To begin, let's distribute the 4, so that the problem becomes -6n-10=-2n+4-12n.
From here, we should combine like-terms. That leaves us with
-6n-10=-14n+4.

We need to isolate the variable, so our next step should be to move all the constants to one side and all the variables to the other.

-6n-10=-14n+4
color(green)(+14n)color(white)()color(purple)(+10)=color(green)(+14n)color(white)(.)color(purple)(+10)

Now we have 8n=14, and if we divide by 8 on both sides we have n=14/8 or 1.75.

Mar 30, 2017

n=7/4

Explanation:

The first step is to distribute the bracket.

rArr-6n-10=-2n+4-12n

rArr-6n-10=-14n+4

Collect terms in n on the left side and numeric values on the right side.

add 14n to both sides.

-6n+14n-10=cancel(-14n)cancel(+14n)+4

rArr8n-10=4

add 10 to both sides.

8ncancel(-10)cancel(+10)=4+10

rArr8n=14

divide both sides by 8

(cancel(8) n)/cancel(8)=14/8

rArrn=14/8=7/4

color(blue)"As a check"

Substitute this value into the equation and if the left side equals the right side then it is the solution.

"left side "=(-6xx7/4)-10=-21/2-10=-41/2

"right side "=(-2xx7/4)+4(1-3xx7/4)

color(white)(right sidexx)=-7/2+4(1-21/4)

color(white)(right sidexx)=-7/2-17=-41/2

rArrn=7/4" is the solution"