1. **State the problem:** Solve the linear equation $4x + 2 = -6$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, whatever you do to one side of the equation, you must do to the other side to keep it balanced. 3. **Step 1:** Subtract 2 from both sides to isolate the term with $x$: $$4x + 2 - 2 = -6 - 2$$ which simplifies to $$4x = -8$$ 4. **Step 2:** Divide both sides by 4 to solve for $x$: $$\frac{4x}{4} = \frac{-8}{4}$$ which simplifies to $$x = -2$$ 5. **Final answer:** $x = -2$