Final answer:
To solve the equation 2|x+2| = |x-1|, consider two cases: when x+2 > 0 and when x+2 < 0. Solve each case separately to find the solutions.
Step-by-step explanation:
To solve the equation 2|x+2| = |x-1|, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: x+2 > 0. In this case, the equation becomes 2(x+2) = x-1.
Solving this equation, we get x = -5.
Case 2: x+2 < 0. In this case, the equation becomes 2(-x-2) = x-1.
Solving this equation, we get x = 3/5.
Therefore, the solutions to the equation are x = -5 and x = 3/5.