Answer: -9 and 13/3
Step-by-step explanation:
To solve the equation x+2|x-1|=11, we need to consider two cases: when x-1 is non-negative and when x-1 is negative.
Case 1: (x-1) ≥ 0
If x-1 is non-negative, then the absolute value of x-1 is equal to x-1. Therefore, the equation becomes:
x + 2(x-1) = 11
x + 2x - 2 = 11
3x - 2 = 11
3x = 13
x = 13/3
So, x = 13/3 is a solution in this case.
Case 2: (x-1) < 0
If x-1 is negative, then the absolute value of x-1 is equal to -(x-1) or 1-x. Therefore, the equation becomes:
x + 2(1-x) = 11
x + 2 - 2x = 11
- x + 2 = 11
- x = 9
x = -9
So, x = -9 is a solution in this case.
