Fill in the blanks of the following
If $x>y$ and $z<0$, then $-x z \ldots-y z$.
If $x > y$ and $z < 0$, then
$xz < yz \quad [\text{since, }z < 0]$
$\Rightarrow \quad -xz > -yz$
Fill in the blanks of the following
If $p>0$ and $q<0$, then $p-q \ldots p$. If $|x+2|>5$, then $x \ldots-7$ or $x \ldots 3$. If $-2 x+1 \geq 9$, then $x \ldots-4$.
If $p > 0$ and $q < 0$,
then $p - q > p$
e.g., consider $2 > 0$ and $-3 < 0$.
$\Rightarrow 2-(-3)=2+3-5 > 2$
Fill in the blanks of the following
If $|x+2|>5$, then $x \ldots-7$ or $x \ldots 3$. If $-2 x+1 \geq 9$, then $x \ldots-4$.
$$\begin{aligned} &\text { If }|x+2|>5 \text {, then }\\ &\begin{array}{lc} & x+2<-5 \text { or } x+2>5 \\ \Rightarrow & x<-5-2 \text { or } x>5-2 \\ \Rightarrow & x<-7 \text { or } x>3 \\ \Rightarrow & x \in(-\infty,-7) \cup(3, \infty) \end{array} \end{aligned}$$
Fill in the blanks of the following
If $-2 x+1 \geq 9$, then $x \ldots-4$.
$$\begin{aligned} &\text { If }-2 x+1 \geq 9 \text {, then }\\ &\Rightarrow \quad \begin{aligned} -2 x \geq 9-1 & \Rightarrow-2 x \geq 8 \\ 2 x \leq-8 & \Rightarrow x \leq-4 \end{aligned} \end{aligned}$$