1. **State the problem:** Solve the linear equation $8x + 6 = 22$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable $x$ by performing inverse operations step-by-step. 3. **Step 1:** Subtract 6 from both sides to move the constant term. $$8x + 6 - 6 = 22 - 6$$ $$8x = 16$$ 4. **Step 2:** Divide both sides by 8 to solve for $x$. $$\frac{8x}{\cancel{8}} = \frac{16}{\cancel{8}}$$ $$x = 2$$ 5. **Answer:** The solution to the equation is $x = 2$. This means when $x$ is 2, the original equation holds true.