First, expand the terms in parenthesis on the left side of the inequality. Multiply each term within the parenthesis by the term outside the parenthesis:
#color(red)(8)(6x - 22) - 12 >= 52#
#(color(red)(8) xx 6x) - (color(red)(8) xx 22) - 12 >= 52#
#48x - 176 - 12 >= 52#
#48x - 188 >= 52#
Next, add #color(red)(188)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#48x - 188 + color(red)(188) >= 52 + color(red)(188)#
#48x - 0 >= 240#
#48x >= 240#
Now, divide each side of the inequality by #color(red)(48)# to solve for #x# while keeping the inequality balanced:
#(48x)/color(red)(48) >= 240/color(red)(48)#
#(color(red)(cancel(color(black)(48)))x)/cancel(color(red)(48)) >= 5#
#x >= 5#
