To solve the equation where the difference between an integer x and 6 is 5, we start by understanding what ‘difference’ means in this context. The difference between two numbers means we subtract one from the other.
This can be expressed mathematically as:
|x – 6| = 5
The absolute value equation means that x – 6 can either equal 5 or -5. We need to solve for both cases:
1. If x – 6 = 5:
- Adding 6 to both sides gives us:
- x = 5 + 6
- x = 11
2. If x – 6 = -5:
- Again, adding 6 to both sides gives us:
- x = -5 + 6
- x = 1
Thus, there are two possible values for x: 11 and 1. To summarize, the values of x that satisfy the equation are:
- x = 11
- x = 1