Question: 22 + 54x = 10(6x - 2)
1. **State the problem:** Solve the equation $$22 + 54x = 10(6x - 2)$$ for $$x$$.
2. **Apply the distributive property:** Multiply $$10$$ by each term inside the parentheses:
$$22 + 54x = 10 \times 6x - 10 \times 2$$
which simplifies to
$$22 + 54x = 60x - 20$$
3. **Bring all terms involving $$x$$ to one side and constants to the other:**
Subtract $$54x$$ from both sides:
$$22 + \cancel{54x} - \cancel{54x} = 60x - 54x - 20$$
which simplifies to
$$22 = 6x - 20$$
4. **Add $$20$$ to both sides to isolate the term with $$x$$:**
$$22 + 20 = 6x - 20 + 20$$
which simplifies to
$$42 = 6x$$
5. **Divide both sides by $$6$$ to solve for $$x$$:**
$$\frac{42}{\cancel{6}} = \frac{6x}{\cancel{6}}$$
which simplifies to
$$7 = x$$
6. **Final answer:**
$$x = 7$$