How do you solve #\frac { 2} { 3} ( 3x - 6) = \frac { 3} { 4} ( 2x + 8)#?

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Answer 1 · 2016-11-06T01:09:32

#x=20#

#2/3 (3x-6) = 3/4 (2x+8)#

Let's start by getting rid of the fractions.

Multiply both sides of the equation by the common denominator of the fractions #3 *4 =color(red)(12)#

#color(red)(12) * 2/3 (3x-6) = color(red)(12) * 3/4 (2x+8)#

#24/3 (3x-6)=36/4 (2x+8)#

#8(3x-6) =9 (2x+8)color(white)(aaa)#Distribute

#color(white)(a^2)24x-48 =18x +72#
#-18xcolor(white)(aaaaa)-18xcolor(white)(aaa)#Subtract #18x# from both sides

#6x-48=color(white)a72#
#color(white)(aa)+48color(white)(a^2)+48color(white)(aaa)#Add #48# to both sides

#6x=120#

#(6x)/6=120/6color(white)(aaa)#Divide by #6# on both sides

#x=20#