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How do you solve #(5x)/2 - x = x/14 + 9/7#?

2 Answers
Mar 25, 2018

Answer:

#x = 9/10#

Explanation:

#(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#

Mar 25, 2018

Answer:

#x=9/10#

Explanation:

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#