a) x and y are $I^{+}$ such that $2 \leq x \leq 5 a n d 3 x + 2 y \leq 12$ . List all the possible values of y.

b) Solve the following inequation: $x + \frac{2}{15} \leq \frac{- 8}{15}, x ϵ R$

[6 MARKS]

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Solution

Each subpart: 3 Marks

a) Given $x = 2, 3, 4, 5 a n d 3 x + 2 y \leq 12$
Putting x = 2 in given inequation, we get
$3 \times 2 + 2 y \leq 12$
$\Rightarrow 2 y \leq 6$
$\Rightarrow y \leq 3$
So, $y = {1, 2, 3}$

b)
$x + \frac{2}{15} \leq \frac{- 8}{15}, x ϵ R, \Rightarrow 15 x + 2 \leq - 8 \Rightarrow 15 x \leq - 10 \Rightarrow x \leq \frac{- 2}{3}, x ϵ R$

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5 x - 2 \geq 8

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x + \frac{2}{15} \leq \frac{- 8}{15}, x ϵ R

13 x - 5 < 15 x + 4 < 7 x + 12, x ϵ R

Solve the following inequation:

$13 x - 5 < 15 x + 4 < 7 x + 12, x \in R$ .

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