First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:
#color(red)(4)(2x - 1/2) = color(blue)(-6)(2/3x + 1/2)#
#(color(red)(4) * 2x) - (color(red)(4) * 1/2) = (color(blue)(-6) * 2/3x) + (color(blue)(-6) * 1/2)#
#8x - 2 = -12/3x + (-3)#
#8x - 2 = -4x - 3#
Next, add #color(red)(2)# and #color(blue)(4x)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#color(blue)(4x) + 8x - 2 + color(red)(2) = color(blue)(4x) - 4x - 3 + color(red)(2)#
#(color(blue)(4) + 8)x - 0 = 0 - 1#
#12x = -1#
Now, divide each side of the equation by #color(red)(12)# to solve for #x# while keeping the equation balanced:
#(12x)/color(red)(12) = -1/color(red)(12)#
#(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = -1/12#
#x = -1/12#
