1. **State the problem:** Solve the linear equation $6x + 8 = 2x - 28$ for $x$. 2. **Write down the equation:** $$6x + 8 = 2x - 28$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$6x + 8 - 2x = 2x - 28 - 2x$$ $$\cancel{6x} + 8 - \cancel{2x} = \cancel{2x} - 28 - \cancel{2x}$$ $$4x + 8 = -28$$ 4. **Isolate the constant term on the other side:** Subtract $8$ from both sides: $$4x + 8 - 8 = -28 - 8$$ $$4x + \cancel{8} - \cancel{8} = -28 - 8$$ $$4x = -36$$ 5. **Solve for $x$ by dividing both sides by 4:** $$\frac{4x}{4} = \frac{-36}{4}$$ $$\cancel{4}x/\cancel{4} = -9$$ $$x = -9$$ **Final answer:** $$x = -9$$