1. **State the problem:** We are given the function $X(t) = 3x\left(1-\frac{t}{2}\right) + 1$. We want to understand or simplify this expression. 2. **Clarify the function:** It seems there might be a confusion between the variable $x$ and the function notation. Assuming $x$ is a function of the argument $\left(1-\frac{t}{2}\right)$, the expression is $X(t) = 3 \times x\left(1-\frac{t}{2}\right) + 1$. 3. **Explain the formula:** This is a linear transformation of the function $x$ evaluated at $\left(1-\frac{t}{2}\right)$, scaled by 3 and shifted by 1. 4. **No further simplification is possible without knowing $x(\cdot)$:** To proceed, we need the explicit form of $x(\cdot)$. 5. **Summary:** The function $X(t)$ is defined as $X(t) = 3x\left(1-\frac{t}{2}\right) + 1$ where $x$ is a function evaluated at $1-\frac{t}{2}$, scaled and shifted. Final answer: $X(t) = 3x\left(1-\frac{t}{2}\right) + 1$