How do you solve #(5x)/2 - x = x/14 + 9/7#?
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#(5x)/2 - x = x/14 + 9/7#
Let's get a common denominator for the left side of the equation
#(5x)/2 - x xx 2/2 = x/14 + 9/7#
#(5x - 2x)/2 = x/14 + 9/7#
#(3x)/2 = x/14 + 9/7#
Let's get all the #x#s on the same side
#(3x)/2 - x/14 = 9/7#
Common denominator
#7/7 xx (3x)/2 - x/14 = 9/7#
#(21x)/14 - x/14 = 9/7#
Let's get another common denominator (we don't technically need this, but it makes the math easier later)
#(20x)/14 = 9/7 xx 2/2#
#(20x)/14 = 18/14#
Multiply both sides by #14#
#20x = 18#
Divide by #20# on both sides
#x = 18/20#
#x = 9/10#
We have an equation which has fractions.
#(5x)/2 - x = x/14 + 9/7#
We can get rid of the fractions immediately by multiplying the whole equation by the LCM of the denominators, which is #14#
#(color(blue)(cancel14^7xx)5x)/cancel2 -color(blue)(14xx) x = (color(blue)(cancel14xx)x)/cancel14 + (color(blue)(cancel14^2xx)9)/cancel7" "larr# cancel
#" "35x -14x = x+18#
#35x-14x-x= 18#
#color(white)(xxxxxxxx)20x = 18#
#color(white)(xxxxxxxxx)x= 18/20#
#color(white)(xxxxxxxxx)x=9/10#
