1. **Stating the problem:** We want to create 5 examples of algebraic problems and solve the first one completely. 2. **Example 1:** Solve for $x$ in the equation $$2x + 3 = 11$$. 3. **Formula and rules:** To solve linear equations, isolate $x$ by performing inverse operations. Remember to do the same operation on both sides. 4. **Step-by-step solution:** 1. Subtract 3 from both sides: $$2x + 3 - 3 = 11 - 3$$ $$2x = 8$$ 2. Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{8}{2}$$ $$x = 4$$ 5. **Answer:** $x = 4$ 6. **Examples 2 to 5:** - Example 2: Solve $$3y - 5 = 16$$. - Example 3: Solve $$4z + 7 = 3z + 10$$. - Example 4: Solve $$5a/2 = 15$$. - Example 5: Solve $$6b - 4 = 2b + 8$$. These examples cover basic linear equations with one variable.