How do you solve #9(2 - 3x) - 29 = 8x + 23 - x#?

2 Answers
Jan 8, 2018

See a solution process below:

Explanation:

First rewrite the expression as:

#9(2 - 3x) - 29 = 8x - x + 23#

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

#color(red)(9)(2 - 3x) - 29 = 8x - x + 23#

#(color(red)(9) xx 2) - (color(red)(9) xx 3x) - 29 = 8x - x + 23#

#18 - 27x - 29 = 8x - x + 23#

Then, group and combine like terms on each side of the equation:

#18 - 29 - 27x = 8x - x + 23#

#-11 - 27x = (8 - 1)x + 23#

#-11 - 27x = 7x + 23#

Next, add #color(red)(27x)# and subtract #color(blue)(23)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#-11 - color(blue)(23) - 27x + color(red)(27x) = 7x + color(red)(27x) + 23 - color(blue)(23)#

#-34 - 0 = (7 + color(red)(27))x + 0#

#-34 = 34x#

Now, divide each side of the equation by #color(red)(34)# to solve for #x# while keeping the equation balanced:

#-34/color(red)(34) = (34x)/color(red)(34)#

#-1 = (color(red)(cancel(color(black)(34)))x)/cancel(color(red)(34))#

#-1 = x#

#x = -1#

Jan 8, 2018

#x=-1#

Explanation:

Ok, so there are a few steps to this problem. First we need to combine like terms. Then we will subtract the lowest term from both sides. Let me explain:

We begin with the problem

#9(2-3x)-29=8x-(x-23)#

We need o get rid of the parentheses. To do this we just multiply everything in the parentheses by whats outside of them

#18-27x-29=8x-x+23#

Now we need to combine like terms

#-27x-11=7x+23#

Ok, finally, we need to get #x# on one side with (hopefully) the answer on the other

(Subtract #7x#)
#-27x-11-7x=cancel(7x)+23cancel(-7x)#

#-34x-11=23#

(Add #11#)
#-34xcancel(-11)+cancel(11)=23+11#

#-34x=34#

(Divide by #-34#)
#(cancel(-34x))/cancel(-34)=34/-34#

#x=-1#

Hope this helped!
~Chandler Dowd