How do you solve #|7 - 6x| <= -4#?

1 Answer

Answer:

#x >= +11/6 or x <=1/2 #

Set the +value #<= -4 and -"value" <= -4# and solve.

Explanation:

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.