1. **State the problem:** Solve the linear equation $9x + 8 = 6x + 2$ for $x$. 2. **Write down the equation:** $$9x + 8 = 6x + 2$$ 3. **Isolate the variable terms on one side:** Subtract $6x$ from both sides: $$9x + 8 - \cancel{6x} = \cancel{6x} + 2 - 6x$$ which simplifies to $$9x - 6x + 8 = 2$$ 4. **Simplify the left side:** $$3x + 8 = 2$$ 5. **Isolate the term with $x$ by subtracting 8 from both sides:** $$3x + 8 - 8 = 2 - 8$$ which simplifies to $$3x = -6$$ 6. **Solve for $x$ by dividing both sides by 3:** $$\frac{3x}{\cancel{3}} = \frac{-6}{\cancel{3}}$$ which simplifies to $$x = -2$$ **Final answer:** $$x = -2$$