Solve For X 7Bb465

1. **State the problem:** Solve for $x$ in the equation $$\frac{3x}{4} + 2 = 4x - 1$$. 2. **Write down the equation:** $$\frac{3x}{4} + 2 = 4x - 1$$. 3. **Isolate variable terms on one side:** Subtract $\frac{3x}{4}$ from both sides: $$\frac{3x}{4} + 2 - \frac{3x}{4} = 4x - 1 - \frac{3x}{4}$$ which simplifies to: $$2 = 4x - \frac{3x}{4} - 1$$ 4. **Combine like terms on the right:** Convert $4x$ to $\frac{16x}{4}$ to have a common denominator: $$2 = \frac{16x}{4} - \frac{3x}{4} - 1$$ $$2 = \frac{16x - 3x}{4} - 1$$ $$2 = \frac{13x}{4} - 1$$ 5. **Add 1 to both sides:** $$2 + 1 = \frac{13x}{4} - 1 + 1$$ $$3 = \frac{13x}{4}$$ 6. **Solve for $x$ by multiplying both sides by 4:** $$3 \times 4 = \frac{13x}{\cancel{4}} \times \cancel{4}$$ $$12 = 13x$$ 7. **Divide both sides by 13:** $$\frac{12}{\cancel{13}} = \frac{13x}{\cancel{13}}$$ $$x = \frac{12}{13}$$ **Final answer:** $$x = \frac{12}{13}$$