1. **State the problem:** Solve the linear equation $3x - 8 = 10$ for $x$. 2. **Use the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Add 8 to both sides to cancel the $-8$. 3. **Add 8 to both sides:** $$3x - 8 + 8 = 10 + 8$$ $$3x = 18$$ 4. **Divide both sides by 3 to isolate $x$:** $$\frac{3x}{\cancel{3}} = \frac{18}{\cancel{3}}$$ $$x = 6$$ 5. **Final answer:** $x = 6$. This means the value of $x$ that satisfies the equation is 6.