## Math Problem Statement

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Cubic inequalities

Rational inequalities

Quadratic functions

### Formulas

x^3 + 2x^2 + x + 2 > 0

2/x ≥ x + 1

(x-2)/x^2 ≤ (x+1)/(x+3)

### Theorems

Sign analysis for inequalities

Quadratic formula discriminant

Cross-multiplication and sign analysis

### Suitable Grade Level

Grade 11-12

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