How do you solve the inequality #abs(2-x)-4>=-3# and write your answer in interval notation?

1 Answer
Apr 14, 2017

Answer:

#(-∞, 1] u [3, ∞)#

Explanation:

Solve the inequality first, leaving the abs value alone in one side of the equation and then #x >= (1+2)# and then as we are moving the #-1# to the other side of the equation we have to change the inequality sign to #<=#, leaving #x <= (2-1)#

#|2-x| - 4 >= -3 => |2-x| >= 1 => x >= 3, x <= -1#

As interval notation,

#(-∞, 1] u [3, ∞)#