Final answer:
To solve the equation, we need to isolate the absolute value term first. Then, we can consider two cases for x−1: when it is positive and when it is negative. Solving for x gives us x=6 and x=-6.
Step-by-step explanation:
To solve the equation, −2∣x−1∣+3=(−2/3)x+1, we need to isolate the absolute value term first. Subtracting 3 from both sides gives us -2∣x−1∣=(−2/3)x-2. Then, we can divide both sides by -2 to get ∣x−1∣=(2/3)x+1. Now, we have to consider two cases: when x−1 is positive and when x−1 is negative.
Case 1: x−1 ≥ 0
When x−1 is positive, the absolute value becomes x−1, so we have x−1=(2/3)x+1. Simplifying this equation gives us (1/3)x=2. Solving for x gives us x=6.
Case 2: x−1 < 0
When x−1 is negative, the absolute value becomes -(x−1), so we have -(x−1)=(2/3)x+1. Simplifying this equation gives us (-1/3)x=2. Solving for x gives us x=-6.
Therefore, the solutions to the equation are x=6 and x=-6.