How do you solve #4(x-9)-3(-x+2)=14#?

1 Answer
Oct 23, 2017

Answer:

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Be careful to handle the signs for each term correctly:

#color(red)(4)(x - 9) - color(blue)(3)(-x + 2) = 14#

#(color(red)(4) xx x) - (color(red)(4) xx 9) - (color(blue)(3) xx -x) - (color(blue)(3) xx 2) = 14#

#4x - 36 - (-3x) - 6 = 14#

#4x - 36 + 3x - 6 = 14#

Next, group and combine like terms:

#4x + 3x - 36 - 6 = 14#

#(4 + 3)x + (-36 - 6) = 14#

#7x + (-42) = 14#

#7x - 42 = 14#

Then, add #color(red)(42)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#7x - 42 + color(red)(42) = 14 + color(red)(42)#

#7x - 0 = 56#

#7x = 56#

Now, divide each side of the equation by #color(red)(7)# to solve for #x# while keeping the equation balanced:

#(7x)/color(red)(7) = 56/color(red)(7)#

#(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 8#

#x = 8#