Question: 22 + 54x = (6x - 2)
1. **State the problem:** Solve the equation $$22 + 54x = (6x - 2)$$ for $$x$$.
2. **Rewrite the equation:** Remove parentheses (no change here since it's just one term inside):
$$22 + 54x = 6x - 2$$
3. **Isolate variable terms on one side:** Subtract $$6x$$ from both sides:
$$22 + 54x - 6x = 6x - 2 - 6x$$
$$22 + \cancel{54x - 6x} = \cancel{6x - 6x} - 2$$
$$22 + 48x = -2$$
4. **Isolate constant terms on the other side:** Subtract $$22$$ from both sides:
$$22 + 48x - 22 = -2 - 22$$
$$\cancel{22 - 22} + 48x = -24$$
$$48x = -24$$
5. **Solve for $$x$$:** Divide both sides by $$48$$:
$$\frac{48x}{\cancel{48}} = \frac{-24}{48}$$
$$x = -\frac{24}{48}$$
6. **Simplify the fraction:**
$$x = -\frac{1}{2}$$
**Final answer:** $$x = -\frac{1}{2}$$