What is the solution set for the equation |x - 3| = 2?

The equation |x - 3| = 2 can be interpreted as stating that the distance between x and 3 is 2. This leads us to two scenarios:

1. x - 3 = 2
2. x - 3 = -2

From the first scenario, we solve for x by adding 3 to both sides:

x - 3 = 2 x = 5

In the second scenario, we also add 3 to both sides after flipping the equation:

x - 3 = -2 x = 1

Thus, the solution set includes both x = 5 and x = 1, which corresponds to the first choice. This method of solving absolute value equations is crucial in algebra, as it helps identify all possible solutions given a defined distance from a point on a number line.

The other choices do not satisfy the equation |x - 3| = 2. Only x = 5 or x = 1 fulfills the requirement of being a distance of 2 units from 3.