First, expand the terms on the left side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:
#color(red)(2)(x + 7) + 3 >= 6 + 3x#
#(color(red)(2) xx x) + (color(red)(2) xx 7) + 3 >= 6 + 3x#
#2x + 14 + 3 >= 6 + 3x#
#2x + 17 >= 6 + 3x#
Next, subtract #color(red)(2x)# and #color(blue)(6)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#2x + 17 - color(red)(2x) - color(blue)(6) >= 6 + 3x - color(red)(2x) - color(blue)(6)#
#2x - color(red)(2x) + 17 - color(blue)(6) >= 6 - color(blue)(6) + 3x - color(red)(2x)#
#0 + 11 >= 0 + (3 - color(red)(2))x#
#11 >= 1x#
#11 >= x#
To state the solution in terms of #x# we can reverse or "flip" the entire inequality:
#x <= 11#
