1. Let's create a simple algebraic problem: Solve for $x$ in the equation $$2x + 5 = 13$$. 2. To solve for $x$, first subtract 5 from both sides to isolate the term with $x$: $$2x + 5 - 5 = 13 - 5$$ which simplifies to: $$2x = 8$$ 3. Now, divide both sides by 2 to solve for $x$: $$\frac{2x}{2} = \frac{8}{2}$$ which simplifies to: $$x = 4$$ 4. Therefore, the solution is: $$x = 4$$. --- Let's create a second question on evaluating a quadratic expression for a given $x$: Question: Evaluate $y = x^2 - 3x + 2$ for $x = 3$. 1. Substitute $x = 3$ into the expression: $$y = (3)^2 - 3 \times 3 + 2$$ 2. Calculate step-by-step: $$y = 9 - 9 + 2$$ 3. Simplify: $$y = 2$$ --- Third question on factoring: Question: Factor the quadratic expression $x^2 + 5x + 6$. 1. We look for two numbers that multiply to 6 and add to 5. These numbers are 2 and 3. 2. Therefore, factorization is: $$x^2 + 5x + 6 = (x + 2)(x + 3)$$ 3. Final answer: $$(x + 2)(x + 3)$$