First, expand the terms in parenthesis on the left side of the equation by multiplying each term in parenthesis by the term outside the parenthesis:
color(red)(-7)(-8c + 11) -20 = 19 + 18c + 9c−7(−8c+11)−20=19+18c+9c
(color(red)(-7) xx -8c) + (color(red)(-7) xx 11) -20 = 19 + 18c + 9c(−7×−8c)+(−7×11)−20=19+18c+9c
56c + (-77) -20 = 19 + 18c + 9c56c+(−77)−20=19+18c+9c
56c - 77 - 20 = 19 + 18c + 9c56c−77−20=19+18c+9c
Next, combine like terms on each side of the equation:
56c + (-77 - 20) = 19 + (18 + 9)c56c+(−77−20)=19+(18+9)c
56c + (-97) = 19 + 27c56c+(−97)=19+27c
56c - 97 = 19 + 27c56c−97=19+27c
Then, add color(red)(97)97 and subtract color(blue)(27c)27c from each side of the equation to isolate the cc term while keeping the equation balanced:
56c - 97 + color(red)(97) - color(blue)(27c) = 19 + 27c + color(red)(97) - color(blue)(27c)56c−97+97−27c=19+27c+97−27c
56c - color(blue)(27c) - 97 + color(red)(97) = 19 + color(red)(97) + 27c - color(blue)(27c)56c−27c−97+97=19+97+27c−27c
(56 - color(blue)(27))c - 0 = 116 + 0(56−27)c−0=116+0
29c = 11629c=116
Now, divide each side of the equation by color(red)(29)29 to solve for cc while keeping the equation balanced:
(color(red)(cancel(color(black)(29)))c)/cancel(color(red)(29)) = 4
c = 4
