|x-9|+|x+1|+44 x=8

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.