To solve the equation \( \sqrt{5} - x = x - 3 \), let's follow these steps:

### Step 1: Isolate the variable terms
We want to move all the \( x \)-terms to one side of the equation:

\[
\sqrt{5} - x + x = x - 3 + x
\]

Simplifying this, we get:

\[
\sqrt{5} = 2x - 3
\]

### Step 2: Isolate \( x \)
Next, we'll solve for \( x \) by moving the constant to the other side:

\[
\sqrt{5} + 3 = 2x
\]

So:

\[
x = \frac{\sqrt{5} + 3}{2}
\]

### Final Solution:
The solution to the equation \( \sqrt{5} - x = x - 3 \) is:

\[
x = \frac{\sqrt{5} + 3}{2}
\]

Would you like more details or have any questions?

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Here are some related questions you might find interesting:
1. How do you check if the solution \( x = \frac{\sqrt{5} + 3}{2} \) is correct?
2. Can this type of equation be solved graphically?
3. What are some examples of other equations involving square roots?
4. How do you rationalize the denominator if the square root was in the denominator?
5. What happens if you square both sides of an equation like this one?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation √5 - x = x - 3 with detailed step-by-step instructions. This problem involves isolating variables and basic algebraic manipulation techniques. Suitable for high school students.

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