Question: Solve the inequality \(4x - 3 > 5x + 2\).
Answer: \(x < -5\).
---
Question: Find the value of \( \sin(120^\circ) \) using the unit circle.
Answer: \( \sin(120^\circ) = \frac{\sqrt{3}}{2} \).
---
Question: Calculate the area of a regular hexagon with side length \(9\) units.
Answer: Area = \( \frac{3\sqrt{3}}{2} \times 9^2 \approx 280.95 \) square units.
---
Question: If \(f(x) = \frac{2x - 1}{x + 3}\), find \(f(0)\).
Answer: \(f(0) = -\frac{1}{3}\).
---
Question: Solve the equation \(3 \cdot 2^{x - 2} = 12\).
Answer: \(x = 4\).
---
Question: Determine the solution set for the inequality \(2x^2 - 5x < 3\).
Answer: \(x \in \left(-\infty, \frac{3}{2}\right) \cup \left(2, \infty\right)\).
---
Question: Find the midpoint of the line segment with endpoints \((2, -3)\) and \((8, 5)\).
Answer: Midpoint \(= \left(\frac{2 + 8}{2}, \frac{-3 + 5}{2}\right) = (5, 1)\).
