ExamGOAL
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47

Fill in the blanks of the following

If $\frac{-3}{4} x \leq-3$, then $x \ldots 4$.

Explanation

If $\frac{-3}{4} x \leq-3$

$$\Rightarrow \quad x \geq(-3) \times \frac{4}{-3} \Rightarrow x \geq 4$$

48

Fill in the blanks of the following

If $\frac{2}{x+2}>0$, then $x \ldots-2$.

Explanation

If $\frac{2}{x+2}>0$

$\Rightarrow x > -2$

49

Fill in the blanks of the following

If $x>-5$, then $4 x \ldots-20$.

Explanation

If $x > -5\Rightarrow 4x > -20$

50

Fill in the blanks of the following

If $x>y$ and $z<0$, then $-x z \ldots-y z$.

Explanation

If $x > y$ and $z < 0$, then

$xz < yz \quad [\text{since, }z < 0]$

$\Rightarrow \quad -xz > -yz$

51

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 $x \ldots-4$.

Explanation

If $p > 0$ and $q < 0$,

then $p - q > p$

e.g., consider $2 > 0$ and $-3 < 0$.

$\Rightarrow 2-(-3)=2+3-5 > 2$