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