Question

Solve the inequation and graph the solution set on the number
line : – 8 1⁄2 < - 1⁄2 - 4x ≤ 7 1⁄2 , x Ɛ I

Answer 1

Answer:

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Answer 2

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\: - 8 \: \dfrac{1}{2} < - \dfrac{1}{2} - 4x \leqslant 7 \: \dfrac{1}{2}$

$\rm :\longmapsto\: - \: \dfrac{17}{2} < - \dfrac{(1 + 8x)}{2} \leqslant \: \dfrac{15}{2}$

☆ On multiply by - 2 each term, we get

$\rm :\longmapsto\:17 > 1 + 8x \geqslant - 15$

☆ Subtracting 1 from each term

$\rm :\longmapsto\:17 - 1 \: > 1 + 8x - 1 \: \geqslant - 15 - 1$

$\rm :\longmapsto\:16 \: > 8x \: \geqslant - 16$

☆ On dividing by 8 each term, we get

$\rm :\longmapsto\:2 \: > x \: \geqslant - 2$

$\bf\implies \: - 2 \: \leqslant x \: < \: 2$

$\bf\implies \:x \in \: [- 2, 2)$

Additional Information :-

$\boxed{ \sf \: x > y \implies \: - x < - y}$

$\boxed{ \sf \: x \geqslant y \implies \: - x \leqslant - y}$

$\boxed{ \sf \: x < y \implies \: - x > - y}$

$\boxed{ \sf \: x \leqslant y \implies \: - x \geqslant - y}$

$\boxed{ \sf \: - x \leqslant y \implies \: x \geqslant - y}$