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The number xx is irrational. Which statement about x6x - 6 is true?\newlineChoices:\newline(A)x6x - 6 is rational.\newline(B)x6x - 6 is irrational.\newline(C)x6x - 6 can be rational or irrational, depending on the value of xx.

Full solution

Q. The number xx is irrational. Which statement about x6x - 6 is true?\newlineChoices:\newline(A)x6x - 6 is rational.\newline(B)x6x - 6 is irrational.\newline(C)x6x - 6 can be rational or irrational, depending on the value of xx.
  1. Identify Number 66: Identify the nature of the number 66.66 is a whole number, and all whole numbers are rational numbers.
  2. Properties of Irrational Numbers: Understand the properties of irrational numbers. An irrational number minus a rational number is always irrational.
  3. Apply Property to Problem: Apply the property to the given problem.\newlineSince xx is irrational and 66 is rational, x6x - 6 must be irrational.

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