How do you solve #\frac { x } { 7} - \frac { x } { 3} = \frac { 2} { 3}#?

1 Answer
smendyka
Jun 26, 2017

See a solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(21)# to eliminate the fractions while keeping the equation balanced. #color(red)(21)# is the Lowest Common Denominator (LCD) for the 3 fractions:

#color(red)(21)(x/7 - x/3) = color(red)(21) xx 2/3#

#(color(red)(21) xx x/7) - (color(red)(21) xx x/3) = cancel(color(red)(21))7 xx 2/color(red)(cancel(color(black)(3)))#

#(cancel(color(red)(21))3 xx x/color(red)(cancel(color(black)(7)))) - (cancel(color(red)(21))7 xx x/color(red)(cancel(color(black)(3)))) = 14#

#3x - 7x = 14#

Next, combine like terms:

#(3 - 7)x = 14#

#-4x = 14#

Now, divide each side of the equation by #color(red)(-4)# to solve for #x# while keeping the equation balanced:

#(-4x)/color(red)(-4) = 14/color(red)(-4)#

#(color(red)(cancel(color(black)(-4)))x)/cancel(color(red)(-4)) = -7/2#

#x = -7/2#

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