[3 marks sum]

Question 13 Marks

Solve the following linear in-equation and graph the solution set on a real number line:
2x - 7 < 5x + 2 ≤ 3x + 14, x ∈ R

Answer

2x - 7 < 5x + 2
2x - 5x < 2 + 7
-3x < 9
x > -3
and
5x + 2 ≤ 3x + 14
5x - 3x ≤ 14 - 2
2x ≤ 12
x ≤ 6
Solution set = [-3 < x ≤ 6]

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Question 23 Marks

Solve the following linear in-equation and graph the solution set on a real number line :
3x - 9 ≤ 4x - 7 < 2x + 5, x ∈ R

Answer

3x - 9 ≤ 4x - 7
3x - 4x ≤ -7+9
- x ≤ 2
x ≥ -2
and
4x - 7 < 2x + 5
4x - 2x < 5 +7
2x < 12
x < 6
Solution set = [-2 ≤ x < 6]

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Question 33 Marks

Solve the following linear in-equation and graph the solution set on a real number line:
$2(3x-5) > 5(13-2x), x \in W$

Answer

$2(3 x-5)>5(13-2 x) $
$6 x-10>65-10 x $
$6 x+10 x>65+10 $
$16 x>75 $
$x>\frac{75}{16} $
$c>4 \frac{11}{16}$
Solution set $=\left[x>4 \frac{11}{16}\right]$

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Question 43 Marks

Solve the following linear in-equation and graph the solution set on a real number line:
$3(5x+ 3) \leq 2(9x-17), x \in W$

Answer

$3(5 x+3) \geq 2(9 x-17) $
$15 x+9 \geq 18 x-34 $
$15 x-18 x \geq-34-9 $
$-3 x \geq-43 $
$3 x \leq 43 $
$x \leq \frac{43}{3}$
Solution set $=\left[x \leq \frac{43}{3}\right]$

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Question 53 Marks

Solve the following linear in-equation and graph the solution set on a real number line:
$>2x - 11 \leq 7 - 3x, x \in N$

Answer

$2 x-11 \leq 7-3 x, x \in N$
$2 x-11 \leq 7-3 x$
$2 x+3 x \leq 7+11$
$5 x \leq 18$
$x \leq \frac{18}{5}$
$x \leq 3.6 $
Since $x \in N$
Solution Set $=\{1,2,3\}$

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Question 63 Marks

If $\frac{2 x +7}{3} \leq \frac{5 x +1}{4}$, find the smallest value of $x$, when:
(i) $x \in R$
(ii) $x \in Z$

Answer

$\frac{2}{x^2}-\frac{5}{x}+2=0$
$ 2-5 x+2 x^2=0$
$2 x^2-5 x+2=0 $
$x^2-\frac{5}{2} x+1=0$
$ x^2-2 x-\frac{1}{2} x+1=0 $
$ x(x-2)-\frac{1}{2}(x-2)=0$
$ (x-2)\left(x-\frac{1}{2}\right)=0 $
$ (x-2)=0,\left(x-\frac{1}{2}\right)=0 $
$ x=2, x=\frac{1}{2}$

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Mathematics [3 marks sum]

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