How do you solve #x/6 = x/7 + 5#?

1 Answer
Apr 16, 2017

Answer:

See the entire solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(42)# to eliminate the fractions while keeping the equation balanced. #color(red)(42)# (or #7 xx 6#) is the Least Common Denominator for the two fractions:

#color(red)(42) xx x/6 = color(red)(42)(x/7 + 5)#

#cancel(color(red)(42)) 7 xx x/color(red)(cancel(color(black)(6))) = (color(red)(42) xx x/7) + (color(red)(42) xx 5)#

#7x = (cancel(color(red)(42)) 6 xx x/color(red)(cancel(color(black)(7)))) + 210#

#7x = 6x + 210#

Now, subtract #color(red)(6x)# from each side of the equation to solve for #x# while keeping the equation balanced:

#-color(red)(6x) + 7x = -color(red)(6x) + 6x + 210#

#(-color(red)(6) + 7)x = 0 + 210#

#1x = 210#

#x = 210#