[3 marks sum]

Question 13 Marks

Solve and graph the solution set on a number line: $x - 5 < -2; x \in N.$

Answer

$x-5<-2$
$\Rightarrow x-5+5<-2+5 \ ($Adding $5$ to both sides$)$
$\Rightarrow x<3$
$\therefore$ The required graph is:

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Question 23 Marks

Solve : $7 > 3x - 8 ; x \in N.$

Answer

$7 > 3x – 8\Rightarrow 7 – 3x > 3x – 3x – 8 ($Subtracting $3x)$
$\Rightarrow 7 – 7 – 3x > 3x – 3x – 8 – 7 ($Subtracting $7)$
$\Rightarrow -3x > -15$
$\Rightarrow x < 5 ($Dividing by $-3)$
Required Answer $= \{1, 2, 3, 4\}$
Note : Division by negative number reverses the inequality.

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Question 33 Marks

If the replacement set $= \{- 6,. - 3, 0, 3, 6, 9\};$ find the truth set of the following : $ 2x - 1 > 9$

Answer

$2x – 1 > 9$
$\Rightarrow 2x – 1 + 1 > 9 + 1 ($Adding $1)$
$\Rightarrow 2x > 10$
$\Rightarrow x > 5 ($Dividing by $2)$
$\Rightarrow x > 5$
Required answer $= \{6, 9\}$

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Question 43 Marks

If the replacement set is the set of natural numbers, solve : $4x + 1 \geq 17$

Answer

$4 x+1 \geq 17$
$ \Rightarrow 4 x+1-1 \geq 17-1 ($Subtracting$)$
$ \Rightarrow 4 x \geq 16$
$ \Rightarrow \frac{4 x}{4} \geq \frac{16}{4} ($Dividing by $4 \text { ) }$
$ \Rightarrow x \geq 4$
Required answer $=\{4,5,6, \ldots\}$

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Question 53 Marks

If the replacement set is the set of natural numbers, solve : $3x - 4 > 6$

Answer

$3x – 4 > 6$
$3x – 4 + 4 > 6 + 4 ($Adding $4)$
$\Rightarrow 3x > 10$
$\frac{3 x}{3}>\frac{10}{3} \ldots ($Dividing by $3 )$
$\Rightarrow x >\frac{10}{3}$
$\Rightarrow x>3 \frac{1}{3}$
Required answer $= \{ 4, 5, 6, …\}$

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Question 63 Marks

Solve: $4x - 5 > 10 - x, x \in \{0, 1, 2, 3, 4, 5, 6, 7\}.$

Answer

$4 x-5>10-x, x \in N .$
$ \Rightarrow 4 x+x>10+5$
$ \Rightarrow 5 x>15$
$ \Rightarrow x>\frac{15}{5}=3$
$ \therefore x=4,5,6,7$
Solution set $=\{4,5,6,7\}$

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Question 73 Marks

Solve the inequation $-3 + x < 2, x \in N.$

Answer

$-3 + x < 2, x \in N.$
$\Rightarrow x < 2 - (-3)$
$\Rightarrow x < 2 + 3$
$\Rightarrow x < 5$
$\therefore x = 1, 2, 3, 4 (\because x \in N)$
$\therefore$ Solution set $= \{1, 2, 3, 4\}$

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MATHS [3 marks sum]

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