How do you solve #\frac { 1} { 3} ( 9- 6x ) = x#?

2 Answers
Mar 13, 2018

Answer:

The solution is #x=1#.

Explanation:

First, multiply both sides by #3#. Then, add #6x# to both sides. Lastly, divide both sides by #9#. Here's how it looks:

#1/3(9-6x)=x#

#color(blue)(3*)1/3(9-6x)=color(blue)(3*)x#

#color(red)cancelcolor(blue)3color(blue)\*1/color(red)cancelcolor(black)3(9-6x)=color(blue)(3*)x#

#1(9-6x)=color(blue)3x#

#9-6x=3x#

#9-6xcolor(blue)+color(blue)(6x)=3xcolor(blue)+color(blue)(6x)#

#9color(red)cancelcolor(black)(-6xcolor(blue)+color(blue)(6x))=3xcolor(blue)+color(blue)(6x)#

#9=3x+6x#

#9=9x#

#9color(blue)(div9)=9xcolor(blue)(div9)#

#1=9xcolor(blue)(div9)#

#1=x#

That's the solution. Hope this helped!

Mar 13, 2018

Answer:

#x=1#

Explanation:

A few ways, the simplest would be to first move the #1/3# to the other side so it becomes #xx3#. So now the equation is

#9-6x=3x#

Then move the #-6x# to the other side of the equals sign to make

#9= 3x+6x#

#9=9x#

Then divide both sides by #9# (take the #9x# which is #9# multiplied by #x# back to the other side) to make

#(9x)/9 = 9/9#

#x=1#

Another way to do it is to actually divide the #9# and #6# by #3# since they are divisible making

#3-2x=x#

Using the same method above this would make

#3=3x#

Making #x=1# again.