1. **State the problem:** Solve the linear equation $3x - 12 = -x + 44$ for $x$. 2. **Write down the equation:** $$3x - 12 = -x + 44$$ 3. **Add $x$ to both sides to get all $x$ terms on one side:** $$3x + x - 12 = -x + x + 44$$ $$4x - 12 = 44$$ 4. **Add 12 to both sides to isolate the $x$ term:** $$4x - 12 + 12 = 44 + 12$$ $$4x = 56$$ 5. **Divide both sides by 4 to solve for $x$:** $$\frac{\cancel{4}x}{\cancel{4}} = \frac{56}{4}$$ $$x = 14$$ 6. **Final answer:** $$x = 14$$