Let's break down the equation and the steps involved, along with the rational explanations for each step.
Given the equation:
\[ n + (n - 1.5) = 8 \]
**Step 1: 2n - 1.5 = 8**
- **Rational:** This step combines the terms \( n + (n - 1.5) \) into a single equation by adding the two \( n \) terms together and then simplifying the equation. The expression \( n + n = 2n \) and the constant term \(-1.5\) remains, leading to \( 2n - 1.5 = 8 \).
**Step 2: 2n = 9.5**
- **Rational:** In this step, we isolate \( 2n \) by adding \( 1.5 \) to both sides of the equation. This leads to \( 2n - 1.5 + 1.5 = 8 + 1.5 \), which simplifies to \( 2n = 9.5 \).
**Step 3: n = 4.75**
- **Rational:** Here, we solve for \( n \) by dividing both sides of the equation by \( 2 \). This means \( n = \frac{9.5}{2} \), which simplifies to \( n = 4.75 \).
So the full explanations for each step are as follows:
1. **Step 1:** 2n - 1.5 = 8 **Rational:** Combines terms to simplify the equation.
2. **Step 2:** 2n = 9.5 **Rational:** Isolates \( 2n \) by adding \( 1.5 \) to both sides.
3. **Step 3:** n = 4.75 **Rational:** Solves for \( n \) by dividing by \( 2 \).