SOLUTION: TRUE or FALSE. Write T if the statement is true. Otherwise, give a counterexample that shows the statement false. 1. For all numbers x, x^3 ≥ x 2. For all numbers x, |x

Algebra ->  Testmodule -> SOLUTION: TRUE or FALSE. Write T if the statement is true. Otherwise, give a counterexample that shows the statement false. 1. For all numbers x, x^3 ≥ x 2. For all numbers x, |x      Log On


   

Question 1184617: TRUE or FALSE. Write T if the statement is true. Otherwise, give a counterexample that shows the statement false.
1. For all numbers x, x^3 ≥ x
2. For all numbers x, |x + 3| = |x| + 3

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1. For all numbers x, x^3 ≥ x
2. For all numbers x, |x + 3| = |x| + 3
Neither of those is true for all x.

A counter-example for 1 is x = 0.1

x3 = 0.13 = 0.001

But x3 ≥ x becomes 0.13 ≥ 0.1 which is FALSE,
since 0.13 = 0.001 < 0.1

A counter-example for 2 is x = -1

|-1 + 3| = |-1| + 3
     |2| =    1 + 3
       2 = 4

Which is FALSE.

Edwin