What are the possible values of x if the difference between x and 9 is 6?

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To solve the problem of finding all possible values of x where the difference between x and 9 is 6, we can represent this mathematically. The statement ‘the difference between x and 9 is 6’ can be translated into the following equation:

|x – 9| = 6

This absolute value equation implies two separate cases:

  1. Case 1: x – 9 = 6

    2. In this case, we can solve for x:

    • Add 9 to both sides: x = 6 + 9
    • This simplifies to: x = 15
  2. Case 2: 9 – x = 6

    3. In this case, we similarly solve for x:

    • Subtract 9 from both sides: -x = 6 – 9
    • This simplifies to: -x = -3
    • Multiplying both sides by -1 yields: x = 3

Thus, the two possible values of x that satisfy the original equation are:

  • x = 15
  • x = 3

In conclusion, the possible integer values of x such that the difference between x and 9 is 6 are 3 and 15.

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