How do you solve #4(5k+3)+3(-4k-4)=-48# using the distributive property?

1 Answer
Feb 16, 2017

Answer:

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Be careful to manage the signs of the individual terms correctly:

#color(red)(4)(5k + 3) + color(blue)(3)(-4k - 4) = -48# becomes:

#(color(red)(4) xx 5k) + (color(red)(4) xx 3) - (color(blue)(3) xx 4k) - (color(blue)(3) xx 4) = -48#

#20k + 12 - 12k - 12 = -48#

Next, group and combine like terms on the left side of the equation:

#20k - 12k + 12 - 12 = -48#

#(20 - 12)k + 0 = -48#

#8k = -48#

Now, divide each side of the equation by #color(red)(8)# to solve for #k# while keeping the equation balanced:

#(8k)/color(red)(8) = -48/color(red)(8)#

#(color(red)(cancel(color(black)(8)))k)/cancel(color(red)(8)) = -6#

#k = -6#