SOLUTION: Professor I'm having trouble with solving absolute value equations and inequalities. Hopefully this is clear. /z-2/ > 0 (A) - infinity, +infinity. (B) 0 (C) 2,-2 or (D) - infi

Algebra ->  Test -> SOLUTION: Professor I'm having trouble with solving absolute value equations and inequalities. Hopefully this is clear. /z-2/ > 0 (A) - infinity, +infinity. (B) 0 (C) 2,-2 or (D) - infi      Log On


   



Question 647543: Professor I'm having trouble with solving absolute value equations and inequalities. Hopefully this is clear. /z-2/ > 0
(A) - infinity, +infinity. (B) 0 (C) 2,-2 or (D) - infinity, 2 and 2, infinity

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28z-2%29+%3E+0+ = %28z-2%29+%3E0 and -%28z-2%29+%3E+0
i)
z-2%3E0
z+%3E+2
ii)
-%28z-2%29%3E0
Recall when dividing or multiplying by a negative number, it switches the way the inequality points.
%28z-2%29%3C0
z%3C2
So we have that z<2 and z>2. The answer may be clearer if we put this in interval notation.
So z exists in (-infinity,2) U (2,infinity). U is the union of sets symbol.
D.