1. **State the problem:** We are asked to provide full solutions, but since no specific problem is given, I will demonstrate a full solution to a common algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. **Formula and rules:** To solve a linear equation, we isolate the variable $x$ by performing inverse operations. Important rules: - Addition and subtraction cancel each other. - Multiplication and division cancel each other. 3. **Step-by-step solution:** - Start with the equation: $$2x + 3 = 11$$ - Subtract 3 from both sides to isolate the term with $x$: $$2x + 3 - 3 = 11 - 3$$ $$2x = 8$$ - Divide both sides by 2 to solve for $x$: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{8}{2}$$ $$x = 4$$ 4. **Explanation:** We first removed the constant term 3 by subtracting it from both sides, keeping the equation balanced. Then, we divided both sides by the coefficient of $x$, which is 2, to isolate $x$. The cancellation shows the division of 2 on both numerator and denominator. 5. **Final answer:** $$x = 4$$