First, remove all of the terms on the left side of the inequality from parenthesis. Be careful to handle the signs of each individual term correctly:
#-3 - x + 5 - 5x < -22#
Next, group and combine like terms on the left side of the inequality:
#-x - 5x + 5 - 3 < -22#
#-1x - 5x + 5 - 3 < -22#
#(-x - 5)x + (5 - 3) < -22#
#-6x + 2 < -22#
Then subtract #color(red)(2)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#-6x + 2 - color(red)(2) < -22 - color(red)(2)#
#-6x + 0 < -24#
#-6x < -24#
Now, divide each side of the inequality by #color(blue)(-6)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative numbers we must reverse the inequality operator:
#(-6x)/color(blue)(-6) color(red)(>) (-24)/color(blue)(-6)#
#(color(blue)(cancel(color(black)(-6)))x)/cancel(color(blue)(-6)) color(red)(>) 4#
#x > 4#
