123

Apuntes

• Subtopic: Solving Inequalities Given the inequality: $$\frac{2x-3}{5} > \frac{x+1}{2}$$ Multiply both sides by 10 to eliminate the fractions: $$2(2x-3) > 5(x+1)$$ Simplify: $$4x - 6 > 5x + 5$$ Rearrange the terms: $$4x - 5x > 5 + 6$$ Simplify further: $$-x < 11$$ Multiply by -1 (remember to reverse the inequality sign): $$x < -11$$ • Subtopic: Least Common Multiple (LCM) To find the least common multiple (LCM) of 5 and 2, list the multiples: 5: 5, 10, 15, 20, 25, ... 2: 2, 4, 6, 8, 10, ... The LCM is 10. • Subtopic: Converting Degrees to Radians Convert 360° to radians: $$360° = \frac{180 \times \pi}{360} \times x$$ Solve for \(X\): $$X = \frac{360 \cdot \pi}{180} = 2\pi$$ • Subtopic: Solving Linear Equations Given: $$L_1 = 6x$$ $$L_2 = 3x + 6x = 180$$ Combine like terms: $$9x = 180$$ Solve for \(x\): $$x = \frac{180}{9} = 20$$ • Subtopic: Trigonometric Functions Calculate: $$\sin(60°) + \cos(60°)$$ Using known values: $$\frac{\sqrt{3}}{2} + \frac{1}{2} = \frac{3 + 1}{2} = \frac{4}{2} = 2$$ • Subtopic: Trigonometric Identities Calculate: $$\cos(60°) \cdot \tan(45°)$$ Using known values: $$\frac{1}{2} + \frac{\sin 45}{\cos 45}$$ Simplify: $...