# Inequalities

#### Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.

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### 2022 NYJC Promo Q1

2022 NYJC Promo Q1 (i) Solve the inequality $ln left( x+1 right)le frac{4}{x}$. [3] (ii) Hence solve the inequality $cos x+1le {{text{e}}^{4sec x}}$ for $0<x<pi$. [3] Suggested Video Solutions

### 2022 TJC Promo Q2

2022 TJC Promo Q2 Solve the inequality $frac{x-2k}{{{x}^{2}}-k}le 0$ in terms of $k$ given that (i) $k$ is a real constant greater than $1$. [3] (ii) $k$ is a negative

### 2022 ASRJC Promo Q2

2022 ASRJC Promo Q2 Using an algebraic method, solve $frac{{{x}^{2}}+2x+3}{{{x}^{2}}+x-2}ge 1$. [4] Suggested Video and Handwritten Solutions Continue reading

### 2022 VJC Promo Q2

2022 VJC Promo Q2 (i) Show that ${{x}^{2}}+2x+2$ is always positive for all real values of $x$. [1] (ii) Without using a calculator, solve the inequality $frac{x-12}{{{x}^{2}}+3x-10}>1$. [3] Suggested Video

### 2022 RI Promo Q2

2022 RI Promo Q2 Without using a calculator, solve the inequality $3x+1le frac{{{x}^{2}}+2}{x}$. [5] Suggested Video and Handwritten Solutions Continue reading

2022 YIJC Promo Q2 (a) Using an algebraic method, solve the inequality $2x-1le frac{5}{x-2}$. [3] (b) Hence, solve (i) $2{{text{e}}^{x}}-1le frac{5}{{{text{e}}^{x}}-2}$, [2] (ii) $2x+1ge frac{5}{x+2}$. [2] Suggested Video Solutions Suggested Handwritten