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.Com
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)   (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
RELATED QUESTIONS

is the following conditional statement true or false? If false provide a counterexample. (answered by xinxin)
For all integers a,b,and c, if a = b then a/c = b/c. Provide a counterexample that shows (answered by Edwin McCravy)
Determine whether the statement is true or false. If it is false, explain why or give an... (answered by ikleyn)
Find a counterexample that shows the statement is false. For every number n, 2^n>n... (answered by HyperBrain)
decide if the statement is true or false -(-23) >... (answered by rfer)
Given the following conditional statement, write the converse, the inverse, and the... (answered by solver91311)
Determine whether the statement is true or false. If it is false, explain why or give an... (answered by Boreal)