[45] The solution set of the equation ∣𝑥–1∣=𝑥–1∣x–1∣=x–1 is the set of all values of 𝑥x such that:

The equation given is |x - 1| = x - 1.

The absolute value function |x - 1| can be split into two cases:

1. When (x - 1) is positive or zero, |x - 1| = x - 1. This means x - 1 ≥ 0, so x ≥ 1.

2. When (x - 1) is negative, |x - 1| = -(x - 1). However, this case will not give us a solution because if we substitute |x - 1| with -(x - 1) in the original equation, we get -(x - 1) = x - 1, which simplifies to -x + 1 = x - 1. This further simplifies to 2x = 2, which gives x = 1. But this contradicts our assumption that x < 1 for this case.

So, the solution set of the equation |x - 1| = x - 1 is the set of all x such that x ≥ 1.