How do you solve #\frac { 7y } { 6} - 3= \frac { 5y } { 4}#?

1 Answer
smendyka
Jan 29, 2017

See the entire solution process below:

Explanation:

First, multiply both sides of the equation by #color(red)(12)# (the least common denominator of the two fractions) to eliminate the fractions while keeping the equation balanced. Eliminating the fractions will make solving the equation easier.

#color(red)(12)((7y)/6 - 3) = color(red)(12) xx (5y)/4#

#(color(red)(12) xx (7y)/6) - (color(red)(12) xx 3) = cancel(color(red)(12))3 xx (5y)/color(red)(cancel(color(black)(4)))#

#(cancel(color(red)(12))2 xx (7y)/color(red)(cancel(color(black)(6)))) - 36 = 15y#

#14y - 36 = 15y#

Next, subtract #color(red)(14y)# from each side of the equation to solve for #y#:

#14y - 36 - color(red)(14y) = 15y - color(red)(14y)#

#14y - color(red)(14y) - 36 = 1y#

#0 - 36 = y#

#-36 = y#

#y = -36#

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