How do you solve #3(x-18)=5(x-12)#?

1 Answer
Mar 25, 2018

Answer:

#x=3#

Explanation:

#3(x-18)=5(x-12)#

Let's expand the equation by doing the multiplication
#3x-54=5x-60#

Now if we add to both sides #54#, this number will be moved from the left to the right
#color(red)(+54)+3x-54=5x-60color(red)(+54)#

#3x=5x-60+54#

Same thing can be applied with #5x#
#color(red)(-5x)+3x=5x-60+54color(red)(-5x)#

#3x-5x=-60+54#

And what we have to do now is just the sum of the similiar terms
#-2x=-6#

Multiplying both term by #-1#, we gain an equation with positive #x#
#color(blue)(-1)*-2x=-6*color(blue)(-1)#

#2x=6#

And to finally get the result we can divide both term by #2#
#2/\color(blue)(2)x=6/color(blue)(2)#

x=3

To check whether the result it's right, just plug in the value in the initial equation. If the left and right quantity are the same we did a good job.