The absolute value can be either a negative or a positive value. It is the distance from the value to zero. So the answer that comes out is the same regardless if the answer inside is negative or positive.
Set # +1 xx ( 7 - 6x) <= -4# and solve for the positive value.
This gives
# 7- 6x <= -4 " "# subtract -7 from both sides.
# 7-7 - 6x <= -4 -7" " # This gives
# -6x <= -11 " "# divide everything by -1 . The sign will change.
# (- x)/-1 >= (-11)/(6xx-1)" " # This gives
# x >= + 11/6 #
#( -1)/-1 = +1 # the opposite of -a - is +a (Dividing by a negative always gives you the opposite of what you start with)
When you divide an inequality by a negative number the inequality sign in the middle changes around.
# (-11)/(-1 xx6) = + 11/6# (Dividing by a negative always gives you the opposite sign of what you start with)
Then set # -1( 7-6x ) <= -4" "# and solve for x .This gives
#-7 + 6x <= -4" "# add seven to both sides
#-7 +7 + 6x <= -4 + 7 " "# this gives
#6x <= + 3 " " # Divide both sides by 6
# (6x)/6<= +3/6" "# this gives
#x <= 1/2#
Note that as the x is positive, dividing by +1 would not change any of the values, so is not necessary.
