Question

Select the graph that would represent the best presentation of the solution set for |z| > (1/2).

(I could not all the pics, so if it's none of these just let me know)

Answer 1

Answer: Graph 4

Step-by-step explanation: Because "[z]" is greater than the absolute value of 1/2, any number that is not in between -1/2 and 1/2 is [z]. This is also known as an "or" statement for z can be greater than 1/2 "or" less than -1/2.

[Z]>1/2 (Given)

Plug-in points for "z":

[.25] =.25 & -.25 (subs prop of inequality)

-1/2 <.25 < 1/2 This is an "and" statement, where the line would overlap. So this solution is incorrect

Next, try another number

[1] = -1,1

-1/2<1>1/2 This is an "or" statement meaning the solution can be either less than -1/2 or greater than 1/2 So this would be a solution to the problem