Question

1) Fill in the blanks

If $-4x\ge 12,$ then \(x-3 \).

2) Fill in the blanks

If $\frac{-3x}{4}\le -3$, then \( x 4 \).

3) Fill in the blanks

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

4) Fill in the blanks

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

5) Fill in the blanks

If $x>y,andz<0$ then \( -xz -yz \)

6) Fill in the blanks

If $p>0,andq<0$, then \( p-q p \).

7) Fill in the blanks

If $|x+2|>5$ then, \( x -7~or~x 3 \)

8) Fill in the blanks:

If $-2x+1\ge 9$ then \( x -4 \)

• A. >
• B. >
• C. >
• D. \leq
• E. \leq
• F. >
• G. \geq
• H. >

Answer 1

Answer: (A), (B), (C), (D), (E), (F), (G), (H)

1) Given: $-4x\ge 12$
Sign of inequality changes when its both sides are divided by a negative number
$\Rightarrow x\le -3$

[Dividing the both inequation by -4]

Hence, $x\le -3$

2) Given $\frac{-3x}{4}\le -3$

$\Rightarrow -3x\le -12$

[ Multiplying both sides by 4]

$\Rightarrow x\ge 4$

[ Dividing the above inequation by -3 ]

Hence, $x\ge 4$

3) Given $\frac{2}{x+2}>0$

$\Rightarrow x+2>0$

[ $\because$ Ratio of two positive numbers is always positive]

$\Rightarrow x>-2$

Hence, x > -2.

4) Given: x > -5

Multiplying both side of the inequality by 4,
we get

$\Rightarrow 4x>-20$

Hence, 4x > -20.

5) Given : x > y

z < 0

$\Rightarrow -z>0$

Multiplying both sides of the given inequality by -z, we get

$\Rightarrow -xz>-yz$

Here inequality sign is not changed because -z > 0 i.e. -z is positive number.

Hence, -xz > -yz

6) Given : $p>0andq<0$

Since, Sign of inequality changes when its both sides are multiplied by a negative number

$\Rightarrow -q>0$

Add p both sides, we get,

$\Rightarrow p-q>p$

Hence, $p-q>p$.

7) Given : $|x+2|>5$

$\Rightarrow x+2<-5orx+2>5$

$[\because If\left|x\right|>b\Rightarrow x>borx<-b\forall b>0]$

$\Rightarrow x<-5-2orx>5-2$

$\Rightarrow x<-7orx>3$



So, $x\in (-\infty ,-7)\cup (3,\infty )$

i.e, $x<-7orx>3$

8) Given : $-2x+1\ge 9$

$\Rightarrow -2x\ge 9-1$

$\Rightarrow -2x\ge 8$

$\because$ Sign of inequality changes when its both sides are divided by a negative number

$\Rightarrow x\le -4$

Hence, $x\le -4$