1. Since you asked for more examples, let's solve a common algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. Start by isolating $x$ on one side. Subtract 3 from both sides: $$2x + 3 - 3 = 11 - 3$$ which simplifies to $$2x = 8$$. 3. Next, divide both sides by 2 to solve for $x$: $$\frac{2x}{2} = \frac{8}{2}$$ which gives $$x = 4$$. 4. Therefore, the solution to the equation is $x = 4$. Let's do another example: Solve for $x$ in the quadratic equation $$x^2 - 5x + 6 = 0$$. 5. Factor the quadratic: $$x^2 - 5x + 6 = (x - 2)(x - 3) = 0$$. 6. Set each factor equal to zero: $$x - 2 = 0 \Rightarrow x = 2$$ $$x - 3 = 0 \Rightarrow x = 3$$. 7. So, the solutions are $x = 2$ and $x = 3$. These examples illustrate solving linear and quadratic equations step-by-step.