Answer is x < -5; -5 < x < 7; x > 7
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Explanation:
Rule: We cannot divide by zero.
Because of that rule, we'll set the denominator equal to zero and solve for x. This way we can determine the x value(s) that are to be excluded from the domain.
6 - |x-1| = 0
|x-1| = 6
x-1 = 6 or x-1 = -6
x = 6+1 or x = -6+1
x = 7 or x = -5
Those x values are to be excluded from the domain, since they make the denominator zero.
Imagine a number line in which we poked open holes at -5 and 7
- The portion to the left of -5 is x < -5
- The portion between -5 and 7 is -5 < x < 7
- The portion to the right of 7 is x > 7
Combining everything gets us x < -5; -5 < x < 7; x > 7
