1. **State the problem:** Solve the linear equation $8x + 6 = 22$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side by performing inverse operations. Remember to do the same operation on both sides of the equation. 3. **Step 1:** Subtract 6 from both sides to remove the constant term on the left: $$8x + 6 - \cancel{6} = 22 - \cancel{6}$$ which simplifies to $$8x = 16$$ 4. **Step 2:** Divide both sides by 8 to solve for $x$: $$\frac{8x}{\cancel{8}} = \frac{16}{\cancel{8}}$$ which simplifies to $$x = 2$$ 5. **Final answer:** $x = 2$