Let's solve the equation \((x - 1) - (x - 3) = 2\).

1. Start by expanding the equation:
   \[
   (x - 1) - (x - 3) = x - 1 - x + 3
   \]

2. Simplify by combining like terms:
   \[
   x - x - 1 + 3 = 0x + 2 = 2
   \]

3. This simplifies to:
   \[
   2 = 2
   \]

Since the equation simplifies to a true statement, it means that the original equation is an identity. This implies that the equation holds true for any value of \(x\).

Thus, **all real numbers** are solutions to this equation.

Do you want more details or have any questions?

Here are 5 related questions:
1. How would the solution change if the right side of the equation was a different number, say 5?
2. What does it mean when an equation is an identity?
3. Can you provide an example of an equation that has a unique solution instead of infinitely many solutions?
4. How do you solve an equation where both sides are equal but contain different expressions for \(x\)?
5. What are the differences between an equation, an inequality, and an identity?

**Tip:** When simplifying expressions, always combine like terms and carefully distribute any negative signs.

Learn how to solve the equation (x - 1) - (x - 3) = 2 step-by-step. Understand subtraction of algebraic expressions and how identities are formed in equations. Suitable for students in Grades 6-8.

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