Question: Suppose that $3y - 5 = 45$ and $y = 3x - 2$. Which of the following equations is equivalent to $3y - 5 = 45$, but written only in terms of $x$?
1. **State the problem:** We are given two equations: $$3y - 5 = 45$$ and $$y = 3x - 2$$. We need to find an equation equivalent to $$3y - 5 = 45$$ but expressed only in terms of $x$.
2. **Substitute $y$ in terms of $x$:** Since $y = 3x - 2$, substitute this into the first equation:
$$3(3x - 2) - 5 = 45$$
3. **Simplify the left side:**
$$3 \times 3x - 3 \times 2 - 5 = 45$$
$$9x - 6 - 5 = 45$$
4. **Combine like terms:**
$$9x - 11 = 45$$
5. **Result:** The equation equivalent to $$3y - 5 = 45$$ written only in terms of $x$ is:
$$9x - 11 = 45$$
6. **Check the options:** The correct choice is $$9x - 11 = 45$$.