Question: 6 + 8(x - 1) = 2(3x + 4)
1. **State the problem:** Solve the equation $$6 + 8(x - 1) = 2(3x + 4)$$ for $$x$$.
2. **Use the distributive property:** Expand both sides.
$$6 + 8x - 8 = 6x + 8$$
3. **Simplify both sides:** Combine like terms.
$$8x - 2 = 6x + 8$$
4. **Isolate the variable terms:** Subtract $$6x$$ from both sides.
$$8x - \cancel{6x} - 2 = \cancel{6x} + 8$$
$$2x - 2 = 8$$
5. **Isolate the constant term:** Add $$2$$ to both sides.
$$2x - 2 + 2 = 8 + 2$$
$$2x = 10$$
6. **Solve for $$x$$:** Divide both sides by $$2$$.
$$\frac{2x}{\cancel{2}} = \frac{10}{\cancel{2}}$$
$$x = 5$$
**Final answer:** $$x = 5$$