First, subtract #color(red)(8)# from each side of the inequality to isolate the term in parenthesis while keeping the inequality balanced:
#-7(8m + 2) + 8 - color(red)(8) > 106 - color(red)(8)#
#-7(8m + 2) + 0 > 98#
#-7(8m + 2) > 98#
Next, divide each side of the inequality by #color(blue)(-7)# to eliminate the need for parenthesis while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse inequality operator:
#(-7(8m + 2))/color(blue)(-7) color(red)(<) 98/color(blue)(-7)#
#(color(red)(cancel(color(black)(-7)))(8m + 2))/cancel(color(blue)(-7)) color(red)(<) -14#
#8m + 2 color(red)(<) -14#
Then, subtract #color(red)(2)# from each side of the inequality to isolate the #m# term while keeping the inequality balanced:
#8m + 2 - color(red)(2) color(red)(<) -14 - color(red)(2)#
#8m + 0 color(red)(<) -16#
#8m color(red)(<) -16#
Now, divide each side of the inequality by #color(red)(8)# to solve for #m# while keeping the inequality balanced:
#(8m)/color(red)(8) < -16/color(red)(8)#
#(color(red)(cancel(color(black)(8)))m)/cancel(color(red)(8)) < -2#
#m < -2#
