Question: User: 2x - 1= \frac{3}{4}x + 9
1. **State the problem:** Solve the equation $$2x - 1 = \frac{3}{4}x + 9$$ for $x$.
2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equation. We can do this by moving all terms involving $x$ to one side and constants to the other.
3. **Move terms involving $x$ to the left and constants to the right:**
$$2x - \frac{3}{4}x = 9 + 1$$
4. **Simplify the right side:**
$$2x - \frac{3}{4}x = 10$$
5. **Combine like terms on the left:**
Express $2x$ as $\frac{8}{4}x$ to have a common denominator:
$$\frac{8}{4}x - \frac{3}{4}x = 10$$
6. **Subtract the fractions:**
$$\left(\frac{8}{4} - \frac{3}{4}\right)x = 10$$
$$\frac{5}{4}x = 10$$
7. **Isolate $x$ by dividing both sides by $\frac{5}{4}$:**
$$x = \frac{10}{\frac{5}{4}}$$
8. **Simplify the division by a fraction:**
$$x = 10 \times \frac{4}{5}$$
9. **Multiply:**
$$x = \frac{10 \times 4}{5} = \frac{40}{5}$$
10. **Simplify the fraction:**
$$x = 8$$
**Final answer:** $$x = 8$$