Giải câu 5 bài tập hợp các phép toán trên tập hợp

a) Ta có: $2 x+3 \geq 0 \Leftrightarrow x \geq -\frac{3}{2}$

$\Rightarrow$ $E=\left\{x \in \mathbb{R} \mid x \geq \frac{-3}{2}\right\}$

Ta có: $-x+5 \geq 0 \Leftrightarrow x \leq 5$

$\Rightarrow$ $G=\{x \in \mathbb{R} \mid x \leq 5\}$

$\Rightarrow E \cap G=\left\{x \in \mathbb{R} \mid \frac{-3}{2} \leq x \leq 5\right\}$

Vậy $\mathrm{D}=\left\{x \in \mathbb{R} \mid \frac{-3}{2} \leq x \leq 5\right\}$.

b) Ta có $x+2>0  \Leftrightarrow x>-2$

$\Rightarrow$ $E=\left\{x \in \mathbb{R} \mid x >-2\right\}$

Ta có $2 x-9<0 \Leftrightarrow x<\frac{9}{2}$

$\Rightarrow$ $E=\left\{x \in \mathbb{R} \mid x<\frac{9}{2}\right\}$

$\Rightarrow E \cap G=\left\{x \in \mathbb{R} \mid -2<x<\frac{9}{2}\right\}$

Vậy $\mathrm{D}=\left\{x \in \mathbb{R} \mid -2<x<\frac{9}{2}\right\}$.