Question: 4 + \frac{1}{2} x + 3 = 10
1. **State the problem:** Solve the equation $$4 + \frac{1}{2} x + 3 = 10$$ for $$x$$.
2. **Combine like terms:** Add the constants $$4$$ and $$3$$ on the left side.
$$4 + 3 = 7$$
So the equation becomes:
$$7 + \frac{1}{2} x = 10$$
3. **Isolate the term with $$x$$:** Subtract $$7$$ from both sides.
$$7 + \frac{1}{2} x - 7 = 10 - 7$$
$$\frac{1}{2} x = 3$$
4. **Solve for $$x$$:** Multiply both sides by the reciprocal of $$\frac{1}{2}$$, which is $$2$$.
$$2 \times \frac{1}{2} x = 2 \times 3$$
$$\cancel{2} \times \frac{1}{\cancel{2}} x = 6$$
$$x = 6$$
**Final answer:** $$x = 6$$