Question: Solve the following inequality for $v$. Write your answer in simplest form.
$4v - 3 \geq 6v - 5$
1. **State the problem:** Solve the inequality $$4v - 3 \geq 6v - 5$$ for $v$.
2. **Write down the inequality:** $$4v - 3 \geq 6v - 5$$
3. **Isolate variable terms on one side:** Subtract $4v$ from both sides:
$$4v - 3 - 4v \geq 6v - 5 - 4v$$
which simplifies to:
$$-3 \geq 2v - 5$$
4. **Isolate constant terms on the other side:** Add $5$ to both sides:
$$-3 + 5 \geq 2v - 5 + 5$$
which simplifies to:
$$2 \geq 2v$$
5. **Solve for $v$ by dividing both sides by $2$:**
$$\frac{2}{\cancel{2}} \geq \frac{2v}{\cancel{2}}$$
which simplifies to:
$$1 \geq v$$
or equivalently,
$$v \leq 1$$
6. **Final answer:** The solution to the inequality is $$v \leq 1$$.
This means $v$ can be any number less than or equal to $1$.