How do you solve #-5( 2c - 12) + 2= 20- 7c#?

1 Answer
Sep 26, 2017

#c=14#

Explanation:

First, we look at the left side of the equation.

#-5(2c-12)+2#

We will look at #-5(2c-12)# for now and leave out #+2#.
We will distribute parentheses/brackets using: #x(y+z)=xy+xz#

Therefore, #-5(2c-12)# is the same as #-5*2c cancel(+)-5(-12)#

#-5*2c-5(-12)# is the same as #-5*2c+5*12#.

#5*2c=10c# and #5*12=60#.

Therefore, the equation (with the #+2#) would be #-10c+60+2#.

#60+2=62#

#->-10c+62#

Now we put in the right side of the equation together with the left side.

#-10c+62=20-7c#

We subtract #62# from both sides:
#-10c+62color(blue)-color(blue)62=20-7c color(blue)-color(blue)62#

which is #-10c=-7c-42#

Add #7c# to both sides:
#-10c color(blue)+color(blue)7color(blue)c=-7c-42color(blue)+color(blue)7color(blue)c#

Simplify: #-3c=-42#.

Divide both sides by #3#

#(-3c)/(-3)=(-42)/(-3)#

Simplify:
#c=14#