How do you solve #5/x - 3/7 = 1/2#?

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Answer 1 · 2017-09-06T22:23:36

See a solution process below:

First, add #color(red)(3/7)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#5/x - 3/7 + color(red)(3/7) = 1/2 + color(red)(3/7)#

#5/x - 0 = (7/7 * 1/2) + (2/2 * color(red)(3/7))#

#5/x = 7/14 + 6/14#

#5/x = (7 + 6)/14#

#5/x = 13/14#

Because both sides of the equation are a single fraction we can "flip" the fractions:

#x/5 = 14/13#

Now, multiply each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:

#color(red)(5) xx x/5 = color(red)(5) xx 14/13#

#cancel(color(red)(5)) xx x/color(red)(cancel(color(black)(5))) = 70/13#

#x = 70/13#