First, multiply each side of the equation by #color(red)(10)# to eliminate the fractions while keeping the equations balanced. #color(red)(10)# is the Lowest Common Denominator of the three fractions:
#color(red)(10)(1/2x + 1/5) = color(red)(10)(x/10 + 3)#
#(color(red)(10) xx 1/2x) + (color(red)(10) xx 1/5) = (color(red)(10) xx x/10) + (color(red)(10) xx 3)#
#(cancel(color(red)(10))5 xx 1/color(red)(cancel(color(black)(2)))x) + (cancel(color(red)(10))2 xx 1/color(red)(cancel(color(black)(5)))) = (cancel(color(red)(10)) xx x/color(red)(cancel(color(black)(10)))) + 30#
#5x + 2 = x + 30#
Next, subtract #color(red)(2)# and #color(blue)(x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:
#-color(blue)(x) + 5x + 2 - color(red)(2) = -color(blue)(x) + x + 30 - color(red)(2)#
#-color(blue)(1x) + 5x + 0 = 0 + 28#
#(-color(blue)(1) + 5)x = 28#
#4x = 28#
Now, divide each side of the equation by #color(red)(4)# to solve for #x# while keeping the equation balanced:
#(4x)/color(red)(4) = 28/color(red)(4)#
#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 7#
#x = 7#
