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Question

Find the values of $$x$$, which satisfy the inequation $$-2\dfrac {5}{6} < \dfrac {1}{2} - \dfrac {2x}{3} \leq 2, x \in W$$.


Solution

Given: $$-2\dfrac {5}{6} < \dfrac {1}{2} - \dfrac {2x}{3} \leq 2$$
$$\Rightarrow - \dfrac {17}{6} < \dfrac {3 - 4x}{6} \leq 2$$
Multiplying throughout by $$6$$
$$\Rightarrow -17 < 3 - 4x \leq 12$$
$$-17 < 3 - 4x$$ and $$3 - 4x \leq 12$$
$$\Rightarrow 4x < 3 + 17\ \Rightarrow 3 - 12 \leq 4x$$
$$\Rightarrow 4x < 20 \ \Rightarrow -9\leq 4x$$
$$\Rightarrow x < 5\ \Rightarrow -\dfrac {9}{4} < x$$
$$\left \{5 > x \geq \dfrac {-9}{4}\right \}$$
Hence, the solution set is $$\left \{x : x \in W, -\dfrac {9}{4} \leq x < 5\right \}$$
Since $$x$$ is a whole number,
$$\therefore$$ Values of $$x$$ are $$\left \{0, 1, 2, 3, 4\right \}$$

Mathematics

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