How do you solve #-3( x + 5) = x - 9+ 2( 5x + 2)#?

1 Answer
Sep 25, 2017

#x=-5/7#

Explanation:

First, we will look at the left side, which is #-3(x+5)#
We will distribute parentheses/brackets with this:

#x(y+z)=xy+xz#
Therefore, #-3(x+5)# is the same as #-3*xcancel(+)-3*5#

#-3*5=-15# so the equation will now be #-3x-15#.

Let's focus on the right side now.

#x-9+2(5x+2)#

We'll do the same thing as above, distribute parentheses using:
#x(y+z)=xy+xz#.

Therefore, #2(5x+2)=2*5x+2*2# which is the same as #10x+4#
Now, we put back the #x-9+#

Equation now:
#x-9+10x+4#
We first group like terms:
#x+10x+4-9#
Then add:
#11x+4-9#
Then subtract:
#11x-5#

Now we put both sides together to get
#-3x-15=11x-5#

Add #15# to both sides:
#-3x-15color(blue)+color(blue)15=11x-5color(blue)+color(blue)15#
Simplify:
#-3x=11x+10#

Subtract #11x# from both sides:
#-3xcolor(blue)-color(blue)11color(blue)x=11x+10color(blue)-color(blue)11color(blue)x#

Simplify:
#-14x=10#

Divide both sides by #-14#

#(-14x)/(-14)=10/-14#

to get:

#x=-5/7#