1. **State the problem:** Solve the linear equation $$4x + 10 = -26$$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtract or add terms on both sides and divide by the coefficient of $x$. 3. **Step 1: Subtract 10 from both sides** to move the constant term: $$4x + 10 - 10 = -26 - 10$$ $$4x = -36$$ 4. **Step 2: Divide both sides by 4** to solve for $x$: $$x = \frac{-36}{4}$$ 5. **Step 3: Simplify the fraction:** $$x = \frac{\cancel{ -36 }}{\cancel{ 4 }} = -9$$ 6. **Final answer:** $$x = -9$$ This means the value of $x$ that satisfies the equation is $-9$.