Question: Solve the equation for the given variable. If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal.
$$5(2x - 1) = -3x + 4$$
1. **State the problem:** Solve the equation $$5(2x - 1) = -3x + 4$$ for $$x$$.
2. **Apply the distributive property:** Multiply $$5$$ by each term inside the parentheses.
$$5 \times 2x = 10x$$
$$5 \times (-1) = -5$$
So the equation becomes:
$$10x - 5 = -3x + 4$$
3. **Add $$3x$$ to both sides** to get all $$x$$ terms on one side:
$$10x - 5 + 3x = -3x + 4 + 3x$$
$$13x - 5 = 4$$
4. **Add $$5$$ to both sides** to isolate the $$x$$ term:
$$13x - 5 + 5 = 4 + 5$$
$$13x = 9$$
5. **Divide both sides by $$13$$** to solve for $$x$$:
$$x = \frac{9}{13}$$
Intermediate step showing cancellation:
$$x = \frac{\cancel{13} \times \frac{9}{13}}{\cancel{13}} = \frac{9}{13}$$
6. **Final answer:**
$$x = \frac{9}{13}$$
This fraction is already in reduced form, so this is the solution.