We are given the equation:

\[
(x - 1) - 1 = x - 2
\]

### Step 1: Simplify both sides of the equation.
On the left-hand side:
\[
(x - 1) - 1 = x - 2
\]
Simplifying the left side:
\[
x - 1 - 1 = x - 2 \quad \text{(subtracting 1 gives)} \quad x - 2
\]

So the equation now becomes:
\[
x - 2 = x - 2
\]

### Step 2: Analyze the equation.
Both sides of the equation are identical. Therefore, the equation is always true for any value of \(x\).

### Conclusion:
The equation has **infinite solutions**, meaning that any value of \(x\) satisfies the equation.

Would you like further details on this? 

Here are five related questions to explore:

1. How do you solve equations when variables cancel out on both sides?
2. What does it mean if an equation has no solution versus infinite solutions?
3. Can you demonstrate solving a similar equation with a different result?
4. What is the significance of simplifying both sides of an equation first?
5. How do you check if your solution is correct for an equation?

**Tip**: When both sides of an equation simplify to the same expression, it usually indicates that the equation has infinite solutions.

Explore how to solve the linear equation (x – 1) – 1 = x – 2. The equation simplifies to an identity, meaning it has infinite solutions. Learn key concepts like simplifying expressions and understanding identity equations, suitable for Grades 6-8.

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