How do you solve #\frac{x-1}{2}+\frac{x+4}{3}=15#?

1 Answer
smendyka
Jan 30, 2017

See the entire solution process below:

Explanation:

First, multiple each side of the equation by #color(red)(6)# to eliminate the fractions while keeping the equation balanced. This is the lowest common denominator of the two fractions. Eliminating the fractions will make the equation easy to work with.

#color(red)(6)((x - 1)/2 + (x + 4)/3) = color(red)(6) xx 15#

#(color(red)(6) xx (x - 1)/2) + (color(red)(6) xx (x + 4)/3) = 90#

#(cancel(color(red)(6))3 xx (x - 1)/color(red)(cancel(color(black)(2)))) + (cancel(color(red)(6))2 xx (x + 4)/color(red)(cancel(color(black)(3)))) = 90#

#3x - 3 + 2x + 8 = 90#

#3x + 2x - 3 + 8 = 90#

#5x + 5 = 90#

Next, subtract #color(red)(5)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#5x + 5 - color(red)(5) = 90 - color(red)(5)#

#5x + 0 = 85#

#5x = 85#

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

#(5x)/color(red)(5) = 85/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 17#

#x = 17#

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