# The following absolute value inequality is an "OR" situation? True or False?

|17x +2| greater than or equal to 12

I put False? am i wrong?

### 3 Answers

- JOHNLv 74 weeks ago
Yes, the logical scheme here is ‘P or Q’ is a true proposition if either P is true or Q is true. In formal logic ‘P or Q’ = T if either P = T or Q = T or P = T & Q = T. Here the last is not applicable because |17x + 2| = 12 precludes |17x + 12|> 12. We must have exactly one of a < b or a = b or a > b being true. If one is asked to prove that |17x + 12|> 12 and you’ve managed to prove that |17x + 12| ≥ 12, you have more work to do to exclude |17x + 12| = 12. |17x + 12|> 12 is sharper than |17x + 12| ≥ 12.

- davidLv 74 weeks ago
|17x +2| greater than or equal to 12

case 1 -- 17x +2 greater than or equal to 12 17x greater than or equal to 10

x greater than or equal to 10/17

case 2 -- 17x +2 less than or equal to -12

17x less than or equal to -14

x less than or equal to -14 /17

solution does not use the interval from -14/17 thru 10/17 .... it includes the ends of the x line ... so YES this is an "or"