How do you solve # \frac { x } { 3} + \frac { x } { 2} = 10#?

1 Answer
smendyka
May 19, 2017

See a solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(6)# to eliminate the fractions while keeping the equation balanced. #color(red)(6)# is the Lowest Common Denominator of the two fractions:

#color(red)(6)(x/3 + x/2) = color(red)(6) xx 10#

#color(red)(6)/3x + color(red)(6)/2x = 60#

#2x + 3x = 60#

Next, combine the like terms on the left side of the equation:

#(2 + 3)x = 60#

#5x = 60#

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

#(5x)/color(red)(5) = 60/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 12#

#x = 12#

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