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#