First, multiply each side of the equation by #color(red)(2)# to eliminate the fraction while keeping the equation balanced. Hopefully, this will make the equation easier to work with:
#color(red)(2) xx 1/2x = color(red)(2)(3 + x)#
#2/2x = (color(red)(2) xx 3) + (color(red)(2) xx x)#
#1x = 6 + 2x#
Next, subtract #color(red)(1x)# and #color(blue)(6)# from each side of the equation to solve for #x# while keeping the equation balanced:
#-color(blue)(6) + 1x - color(red)(1x) = -color(blue)(6) + 6 + 2x - color(red)(1x)#
#-color(blue)(6) + 0 = 0 + (2 - color(red)(1))x#
#-color(blue)(6) = 1x#
#-6 = x#
#x = -6#
