First, rewrite the left side of the inequality as:
#-2 - 2x - 2 > 6#
#-2 - 2 - 2x > 6#
#-4 - 2x > 6#
Next, add #color(red)(4)# to each side of the inequality to isolate the #x# term while keeping the equation balanced:
#-4 + color(red)(4) - 2x > 6 + color(red)(4)#
#0 - 2x > 10#
#-2x > 10#
Now, divide each side of the inequality by #color(blue)(-2)# to solve for #x# while keeping the inequality balanced. However, because we are dividing an inequality by a negative number we must reverse the inequality operator:
#(-2x)/color(blue)(-2) color(red)(<) 10/color(blue)(-2)#
#(color(red)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<) -5#
#x < -5#
