Final answer:
The statement x³ < x is true for certain values of x, specifically when x is between 0 and 1 or when x is less than 0. It is false for x > 1 or x = 1.
Step-by-step explanation:
The student asked to determine the truth value of the statement for some number x: x³ < x. To evaluate this, we must consider different ranges of x.
For x > 1, the statement is false because when a number greater than 1 is raised to the third power, it becomes larger than the original number. For x = 1, the statement is also false because 1³ is equal to 1, not less than 1.
However, the statement is true for 0 < x < 1 because in this interval, raising x to the third power makes it smaller than x itself since we are dealing with fractions. Lastly, for x < 0, the statement is true as well, because a negative number raised to the third power remains negative and thus is less than the original negative number which is closer to zero.
Therefore, the correct answer is that the statement x³ < x is true for certain values of x, specifically when x is between 0 and 1 or when x is less than 0.