Final answer:
The equation [x-1]=[x] admits a single solution, x = 0.5, which is a rational number. Therefore, the set that best describes the possible values for x is Rational Numbers.
Step-by-step explanation:
To answer the question on the set of numbers that best describes the possible values of [x−1]=[x], let's first understand that the expression within the absolute value symbols, [ ], denotes the absolute value of the number inside. The absolute value of a number is its non-negative value, so both x-1 and x must yield the same non-negative result for the equation to be true.
Since the only value for which x and x-1 are equal non-negative numbers is 0.5, the solution to the equation is not a set but a single rational number. Therefore, option (c) Rational Numbers best describes the set, even though in this case, it’s just one single value, not a set.
To answer the student's question directly:
- The equation [x−1]=[x] has one solution, which is x = 0.5, hence the set of numbers that best describes the possible values for x is Rational Numbers.