How do you solve # 6(m - 2) + 14 = 3(m + 2) - 10 #?

1 Answer
Mar 11, 2017

Answer:

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(6)(m -2) + 14 = color(blue)(3)(m + 2) - 10#

#(color(red)(6) xx m) - (color(red)(6) xx 2) + 14 = (color(blue)(3) xx m) + (color(blue)(3) xx 2) - 10#

#6m - 12 + 14 = 3m + 6 - 10#

#6m + 2 = 3m - 4#

Next, subtract #color(red)(2)# and #color(blue)(3m)# from each side of the equation to isolate the #m# term while keeping the equation balanced:

#6m + 2 - color(red)(2) - color(blue)(3m) = 3m - 4 - color(red)(2) - color(blue)(3m)#

#6m - color(blue)(3m) + 2 - color(red)(2) = 3m - color(blue)(3m) - 4 - color(red)(2)#

#(6 - 3)m + 0 = 0 - 6#

#3m = -6#

Now, divide each side of the equation by #color(red)(3)# to solve for #m# while keeping the equation balanced:

#(3m)/color(red)(3) = -6/color(red)(3)#

#(color(red)(cancel(color(black)(3)))m)/cancel(color(red)(3)) = -2#

#m = -2#