If x-1=0 then x=1. That's it.
If x-1=15 (for example, then x=15+1 (add 1 to each side of the = sign)
Therefore, x=16. Simple.
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The question contains an algebraic expression but there is no equation to solve.
Simplifying an equation often helps solve it.
You need not have x in an algebraic equation. You solve whichever one is the easiest and that depends on the set of equations that you have.
An equation or an inequality can be solved but an expression cannot be solved.
The question contains an algebraic expression but, since there is no equality sign, there is no equation to solve.