[2 Mark Question Answer]

Question 12 Marks

Solve for $x : \frac{ x }{4}+3 \leq \frac{ x }{3}+4$, where $xis$ a negative odd number.

Answer

$\frac{x}{4}+3 \leq \frac{x}{3}+4 $
$\frac{x+12}{4} \leq \frac{x+12}{3} $
$3 x+36 \leq 4 x+48 $
$3 x-4 x \leq 48-36 $
$-x \leq 12 $
$x \geq-12$
Solution set $=\{-11-9-7-5-3-1\}$

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Question 22 Marks

Solve for x : 2x + 7 ≥ 5x - 14, where x is a positive prime number.

Answer

2x + 7 ≥ 5x - 14
2x - 5x ≥ -14 - 7
-3x ≥ -21
3x ≤ 21
x ≤ 7
Solution set = { 2,3,5,7}

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Question 32 Marks

Solve for x : 5x - 14 < 18 - 3x, where x ∈ W

Answer

5x -14< 18 - 3x
5x + 3x < 18 + 14
8x < 32
x < 4
Solution set= {0,1,2,3}

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Question 42 Marks

Solve for x : 7 + 5x > x - 13, where x is a negative integer.

Answer

7 + 5x > x - 13
- x + 5x > - 13 - 7
4x > -20
x > -5
Solution set= { -4, -3, -2,-1}

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Question 52 Marks

Solve for x: 5x - 9 ≤ 15 - 7x , x ∈ W

Answer

5x - 9 ≤ 15 - 7x
5x + 7x ≤ 15 + 9
12 x ≤ 24
x ≤ 2
Solution set= {0, 1,2}

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Question 62 Marks

Solve for x : 3 - 2x ≥ x - 12, x ∈ N

Answer

3 - 2x ≥ x - 12
3 + 12 ≥ X + 2X
15 ≥ 3x
x ≤ 5
Solution set = {1,2,3,4,5}

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Question 72 Marks

Solve for x : 6 - 10x < 36, x ∈ {-3, -2, -1, O, 1, 2}

Answer

6 - 10x < 36
-10x < 36- 6
-10x < 30
10x > -30
x > -3
Solution set = { -2, -1, 0, 1, 2}

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Question 82 Marks

Solve for x in the following in-equation, if the replacement set is R;
9 - 4x ≤ 15 - 7x

Answer

9 - 4x ≤ 15 - 7x
9 - 4x ≤15 - 7x
9 - 15 ≤ 4x - 7x
-6 ≤ -3x
6 ≥ 3x ( multiplying by -1 changes the sign)
x ≥ 2
Since, replacement set is R
Solution set= {x : x ∈ R and x ≤ 2}

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Question 92 Marks

Solve for x in the following in-equation, if the replacement set is R;
2x - 7 ≥ 5x + 8

Answer

2x - 7 ≥ 5x + 8
2x - 7 ≥ 5x + 8
2x - 5x ≥ 8 + 7
-3x ≥ 15
3x ≤ -15
x ≤ -5
Since, replacement set is R
Solution set= {x : x ∈ R and x ≤ -5}

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Question 102 Marks

Solve for x in the following in-equation, if the replacement set is R;
x + 7 ≥ 15 + 3x

Answer

x + 7 ≥ 15 + 3x
x + 7 ≥ 15 + 3x
x - 3x ≥ 15 - 7
-2x ≥ 8
2x ≤ -8
x ≤ -4
Since, replacement set is R
Solution set= {x : x ∈ R and x ≤ -4}

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Question 112 Marks

Solve for x in the following in-equation, if the replacement set is R;
2(3x - 5) ≤ 8

Answer

2(3x - 5) ≤ 8
2(3x - 5) ≤ 8
6x - 10 ≤ 8
6x ≤ 8 + 10
6x ≤ 18
x ≤ 3
Since, replacement set is R
Solution set= {x : x ∈ R and x ≤ 3}

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Question 122 Marks

Solve for x in the following in-equation, if the replacement set is R;
3x + 25 < 8x - 10

Answer

3x + 25 < 8x - 10
3x + 25 < 8x - 10
25 + 10 < 8x - 3x
35 < 5x
x > 7
Since, replacement set is R
Solution set= {x : x ∈ R and x > 7}

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Question 132 Marks

Solve for x in the following in-equation, if the replacement set is R;
$7x + 11 > 16 - 3x$

Answer

$7 x+11>16-3 x$
$7 x+11>16-3 x $
$7 x+3 x>16-11 $
$10 x>5$
$x>\frac{5}{10}=0.5$
Since, replacement set is $R$
Solution set $=\{x: x \in R$ and $x>0.5\}$

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Question 142 Marks

Solve for x in the following in-equation, if the replacement set is R;
$14 - 3x > 5$

Answer

$14-3 x \geq 5 $
$14-3 x \geq 5 $
$-3 x \geq 5-14 $
$3 x \leq 9 \quad \text { ( multiplying by }-1 \text { changes the sign) } $
$x \leq \frac{9}{3} $
$x \leq 3$
Since, replacement set is $R$
Solution set $=\{x: x \in R$ and $x \leq 3\}$

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Question 152 Marks

Solve for x in the following in-equation, if the replacement set is R;
$3x + 2 \leq 11$

Answer

$3 x+2 \leq 11 $
$3 x+2 \leq 11 $
$3 x \leq 11-2 $
$3 x \leq 9 $
$x \leq \frac{9}{3} $
$x \leq 3$
Since, replacement set is $R$
Solution set $=\{x: x \in R$ and $x \leq 3\}$

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Question 162 Marks

Solve for x in the following in-equation, if the replacement set is R;
$2x - 3 < 7$

Answer

$2 x-3<7 $
$2 x-3<7 $
$2 x<7+3 $
$2 x<10 $
$x<\frac{10}{2}$
Since, replacement set is $R$
Solution set $=\{x: x \in R$ and $x<5\}$

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Question 172 Marks

Solve for x in the following in-equation, if the replacement set is R;
$3x >12$

Answer

$3 x>12 $
$3 x>12 $
$x>\frac{12}{3} $
$x>4$
Since, replacement set is $R$
Solution set $=\{x: x \in R$ and $x>4\}$

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Question 182 Marks

Solve for x in the following in equation, if the replacement set is N<10:
5 - 2x < 11

Answer

5 - 2x < 11
5-2x < 11
⇒ -2x < 11-5
⇒ -2x < 6
⇒ x > -3
But { x : x E N; N < 10}
Therefore, solution set x = { 1,2,3,4,5,6, 7 ,8, 9}

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Question 192 Marks

Solve for x in the following in equation, if the replacement set is N<10:
8 - 3x > 2

Answer

8 - 3x > 2
8 - 3x > 2
⇒ -3x > -6
⇒ x > 2
But { x : x E N; N < 10}
Therefore, solution set x = {1,2}

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Question 202 Marks

Solve for x in the following in equation, if the replacement set is N<10:
3x - 5 < 7

Answer

3x - 5 < 7
3x-5 < 7
⇒ 3X <7 + 5
⇒ 3X < 12
⇒ x < 4
But {x : x E N; N < 1 O}
Therefore, solution set x = { 1,2,3,4}

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Question 212 Marks

Solve for x in the following in equation, if the replacement set is N<10:
2x + 1 < 17

Answer

2x + 1 < 17
2x + 1 < 17
⇒ 2x < 17 - 1 16
⇒ x <2
⇒ x < 8
But {x : x E N; N < 10}
Therefore, solution set x = {1,2,3,4,5,6, 7}

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Question 222 Marks

Solve for x in the following in equation, if the replacement set is N<10:
x + 5 > 11

Answer

x + 5 > 11
x+5 >11
⇒ X >11-5
⇒ x > 6
But {x : x E N; N < 1 O}
Therefore, solution set x = {7 ,8, 9}

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Question 232 Marks

If $x + 17 \leq 4x + 9,$ find the smallest value of $x,$ when:
$x \in R$

Answer

$x \in R$
$x+17 \leq 4 x+9$
$x-4 x \leq 9-17$
$-3 x \leq-8$
$3 x \geq 8$
$x \geq \frac{8}{3} $
Since $x \in R$
Smallest value of $x=\left[2 \frac{2}{3}\right]$

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Question 242 Marks

If $x + 17 \leq 4x + 9,$ find the smallest value of $x,$ when:
$x \in Z$

Answer

$ x \in Z$
$x+17 \leq 4 x+9$
$x-4 x \leq 9-17$
$-3 x \leq-8$
$3 x \geq 8$
$x \geq \frac{8}{3}$
Since $x \in Z$
Smallest value of $x=[3]$

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Question 252 Marks

Solve for $x : \frac{ x +3}{3} \leq \frac{ x +8}{4}$, where $x$ is a positive even number.

Answer

$\frac{x+3}{3} \leq \frac{x+8}{4} $
$ 4 x+12 \leq 3 x+24$
$ 4 x-3 x \leq 24-12$
$ x \leq 12$
$ \text { Solution set }=\{2,4,6,8,10,12\}$

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