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.
