How do you solve #8x+15=3x-20#?

3 Answers
May 9, 2018

#x=-7#

Explanation:

show below

#8x+15=3x-20#

#8x-3x=-20-15#

#5x=-35#

#x=-7#

May 9, 2018

The solution to the equation is #x=-7#

Explanation:

Start by getting like terms on the same side of the equation, I'll subtract fifteen from both sides first:

#8x+15=3x-20#
#8x=3x-35#

Next, subtract #3x# from both sides:

#5x=-35#

And finally, divide by #5# on both sides.

#(color(red)(cancel(5))x)/color(red)(cancel(5))=(-35)/5#

The fives on the left cancel each other out (because #(5x)/5=x#), leaving us with this:

#x=(-35)/5#

#x=color(red)(-7)#

May 9, 2018

Re-arrange the equation, and you will find that #x=-7#

Explanation:

First, we'll add and subtract values from both sides such that all of the #x#-terms and their coefficients will end up on one side, and the constants will be on the other:

#8x+15color(red)(-3x)=cancel(3x)-20color(red)(cancel(-3x))#

#8xcolor(red)(-3x)+15=-20#

#5x+15=-20#

#5xcancel(+15)color(red)(cancel(-15))=-20color(red)(-15)#

#5x=-20color(red)(-15)#

#5x=-35#

Now that the equation has been rearranged as we like it, we'll divide both sides by #x#'s coefficient. In this expression, the coefficient is 5:

#(cancel(5)x)/color(red)(cancel(5))=(-35)/color(red)(5)#

#x=(-35)/color(red)(5)#

#color(green)(x=-7)#