How do you solve #3= \frac { 5x - 4} { 3} + \frac { 3x - 1} { 5}#?
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#3=(5x-4)/3+(3x-1)/5#
Multiply all terms by the LCM of #3# and #5# which is #15#.
#3xx15=15xx(5x-4)/3+15xx(3x-1)/5#
#45=5cancel15xx(5x-4)/(1cancel3)+3cancel15xx(3x-1)/(1cancel5)#
#45=5(5x-4)+3(3x-1)#
Open the brackets and simplify.
#45=25x-20+9x-3#
#45=25x+9x-20-3#
#45=(25x+9x)-(20+3)#
#45=34x-23#
Add #23# to both sides.
#45+23=34x-23+23#
#68=34x#
Divide both sides by #34#.
#68/34=(34x)/34#
#(2cancel68)/(1cancel34)=(cancel34x)/cancel34#
#2=x# or #x=2#
Please see the step process below;
#3= \frac { 5x - 4} { 3} + \frac { 3x - 1} { 5}#
First Step: Multiply via the LCM, in this case the LCM #= 15#
#15 (3/1) = 15 ((5x - 4)/3) + 15 ((3x - 1)/5)#
Second Step: Simplify
#15 (3/1) = cancel15^5 ((5x - 4)/cancel3) + cancel15^3 ((3x - 1)/cancel5)#
#15(3) = 5 (5x - 4) + 3 (3x - 1)#
#45 = 25x - 20 + 9x - 3#
Third Step: Collecting like terms
#45 = 25x + 9x - 20 - 3#
#45 = 34x - 23#
#45 + 23 = 34x#
#68 = 34x#
Divide both sides by #34#
#68/34 = (34x)/34#
#68/34 = (cancel34x)/cancel34#
#68/34 = x#
#x = 2#
