Arithmetic mean between x -3 and x + 3 is:

The correct answer is x because the arithmetic mean of two terms is calculated by finding their average.

• Step 1 (Set up the formula): The arithmetic mean formula for two values a and b is (a + b) / 2. Substituting our values gives ((x - 3) + (x + 3)) / 2.
• Step 2 (Simplify the numerator): Combining like terms in the numerator, the -3 and +3 cancel each other out, leaving x + x = 2x.
• Step 3 (Divide by 2): Dividing 2x / 2 cancels out the 2s, which leaves us with x.
• Incorrect Options:
  • -6 is incorrect because it represents the difference between the bounds, not the central average.
  • 6 is incorrect because it is the total distance between the two expressions, not their midpoint.
  • None of these is incorrect because option 3 perfectly satisfies the arithmetic mean definition.