Final answer:
In an equilateral triangle with two sides having lengths x - 1 and -x + 3, the length of the third side is 3 - x, since all sides of an equilateral triangle must have equal length and this is the only option that gives the same length when x is determined to be 2.
Step-by-step explanation:
The student asked which could be the length of the third side of an equilateral triangle if two sides have lengths x - 1 and -x + 3. The two options provided are 3 - x or 2x + 2. Since it's an equilateral triangle, all sides must have equal length. Therefore, we set the lengths equal to each other to find the possible value of x, ensuring that the third side also has a length that matches the other two.
Setting x - 1 equal to -x + 3, we find that x equals 2 after solving the equation 2x = 4. Plugging x = 2 into the provided options, 3 - x becomes 1 (which is the same length as the other sides after plugging x = 2 into them), and 2x + 2 becomes 6, which is not equal to the other sides. Thus, the length of the third side is 3 - x.