Fill in the blanks of the following
If $\frac{-3}{4} x \leq-3$, then $x \ldots 4$.
If $\frac{-3}{4} x \leq-3$
$$\Rightarrow \quad x \geq(-3) \times \frac{4}{-3} \Rightarrow x \geq 4$$
Fill in the blanks of the following
If $\frac{2}{x+2}>0$, then $x \ldots-2$.
If $\frac{2}{x+2}>0$
$\Rightarrow x > -2$
Fill in the blanks of the following
If $x>-5$, then $4 x \ldots-20$.
If $x > -5\Rightarrow 4x > -20$
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 $-3 < 0$.
$\Rightarrow 2-(-3)=2+3-5 > 2$