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

1 Answer
Mar 16, 2018

See a solution process below

Explanation:

First, multiply each side of the equation by #color(red)(4)# to eliminate the fractions while keeping the equation balanced. #color(red)(4)# is used because it is the Lowest Common Denominator for both fractions:

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

#color(red)(4) xx x) + color(red)(4) xx 1/2) = 12/4#

#4x + 4/2 = 12/4#

#4x + 2 = 3#

Next, subtract #color(red)(2)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#4x + 2 - color(red)(2) = 3 - color(red)(2)#

#4x + 0 = 1#

#4x = 1#

Now, divide each side of the equation by #color(red)(4)# to solve for #x# while keeping the equation balanced:

#(4x)/color(red)(4) = 1/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 1/4#

#x = 1/4#