To solve the equation |x-9|+|x+1|+44 = 8, we need to consider the different cases based on the absolute value expressions.
Case 1: x ≥ 9
For x ≥ 9, both absolute values become positive, so the equation simplifies to:
(x-9) + (x+1) + 44 = 8
2x - 8 + 44 = 8
2x + 36 = 8
2x = -28
x = -14
However, x ≥ 9 in this case, so there are no solutions for this part.
Case 2: -1 < x < 9
For -1 < x < 9, the first absolute value is negative and the second is positive, so we need to consider the signs:
-(x-9) + (x+1) + 44 = 8
- x + 9 + x + 1 + 44 = 8
10 + 44 = 8
54 ≠ 8
There are no solutions in this case.
Case 3: x ≤ -1
For x ≤ -1, both absolute values become negative:
-(x-9) - (x+1) + 44 = 8
- x + 9 - x - 1 + 44 = 8
56 = 8
Again, there are no solutions in this case.
Therefore, there are no solutions to the equation |x-9|+|x+1|+44 = 8.
