1. **State the problem:** Solve the linear equation $5a + 2 = -13$ for $a$. 2. **Recall the formula and rules:** A linear equation in one variable can be solved by isolating the variable on one side. We use inverse operations to undo addition, subtraction, multiplication, or division. 3. **Step 1: Subtract 2 from both sides** to isolate the term with $a$: $$5a + 2 - 2 = -13 - 2$$ which simplifies to $$5a = -15$$ 4. **Step 2: Divide both sides by 5** to solve for $a$: $$a = \frac{-15}{5}$$ which simplifies to $$a = -3$$ 5. **Interpretation:** The solution $a = -3$ means that when $a$ is $-3$, the original equation holds true. 6. **Check:** Substitute $a = -3$ back into the original equation: $$5(-3) + 2 = -15 + 2 = -13$$ which matches the right side, confirming the solution is correct.