Solve Linear Equation 0B45Ce

1. **State the problem:** Solve the equation $$1 + \frac{1}{2} (7x - 10) + \frac{1}{2} x = 3x$$ for $x$. 2. **Use the distributive property:** Expand $$\frac{1}{2} (7x - 10)$$ to get $$\frac{1}{2} \times 7x - \frac{1}{2} \times 10 = \frac{7}{2} x - 5$$. 3. **Rewrite the equation:** $$1 + \frac{7}{2} x - 5 + \frac{1}{2} x = 3x$$ 4. **Combine like terms on the left side:** $$1 - 5 + \frac{7}{2} x + \frac{1}{2} x = 3x$$ $$-4 + \frac{8}{2} x = 3x$$ $$-4 + 4x = 3x$$ 5. **Isolate $x$ terms:** Subtract $3x$ from both sides: $$-4 + 4x - 3x = 3x - 3x$$ $$-4 + \cancel{4x} - \cancel{3x} = \cancel{3x} - \cancel{3x}$$ $$-4 + x = 0$$ 6. **Solve for $x$:** Add $4$ to both sides: $$-4 + x + 4 = 0 + 4$$ $$\cancel{-4} + x + \cancel{4} = 4$$ $$x = 4$$ **Final answer:** $$x = 4$$