How do you solve #|7 - 6x|

Question

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

Ethan Adkins · Accepted Answer

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

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

The absolute value, which is the distance from the value to zero, can be either positive or negative. Consequently, the resultant answer remains the same whether the internal answer is positive or negative. Set # +1 xx ( 7 - 6x) <= -4# and solve for the positive value. This provides # 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) The inequality sign in the middle shifts when you divide an inequality by a negative number. # (-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# It should be noted that since the x is positive, dividing by +1 is not required because it would not affect any of the values.

Eva Abramson · Answer

undefined The absolute value of any expression cannot be negative. Therefore, there are no solutions to the inequality |7 - 6x| <= -4.

Savannah Anderson · Answer

undefined The inequality $ |7 - 6x| \leq -4 $ has no solution because the absolute value of any real number is always non-negative, and thus cannot be less than or equal to -4.

How do you solve #|7 - 6x| &lt;= -4#?

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