To solve the equation \( x - 3 = 5 - x \):

1. Start by adding \( x \) to both sides to eliminate \( x \) from the right-hand side:
   \[
   x + x - 3 = 5
   \]
   This simplifies to:
   \[
   2x - 3 = 5
   \]

2. Next, add 3 to both sides to isolate the term with \( x \):
   \[
   2x - 3 + 3 = 5 + 3
   \]
   Simplifying further:
   \[
   2x = 8
   \]

3. Finally, divide both sides by 2 to solve for \( x \):
   \[
   x = \frac{8}{2} = 4
   \]

So, the solution is \( x = 4 \).

Would you like any further details or explanations?

Here are some related questions you could explore:
1. What happens if we subtract \( x \) from both sides instead?
2. How do you verify the solution to the equation?
3. What if the equation was \( 2x - 3 = 10 - x \)?
4. How do we solve equations with fractions?
5. How does adding or subtracting the same value to both sides affect the equation?

**Tip**: Always perform the same operation on both sides of an equation to maintain equality.

Learn how to solve the linear equation X - 3 = 5 - X with this step-by-step guide. This solution covers fundamental algebraic concepts such as simplifying equations and using the addition property of equality. Ideal for students in Grades 6-8.

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