Question

pls tell me the first answer no spaming or else you will be reported.​

Answer 1

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

Given inequality is

$\rm :\longmapsto\: - 3 < - \dfrac{1}{2} - \dfrac{2x}{3} \leqslant \dfrac{5}{6}$

Consider,

$\rm :\longmapsto\: - 3 < - \dfrac{1}{2} - \dfrac{2x}{3}$

$\rm :\longmapsto\: - 3 < \dfrac{ - 3 - 4x}{6}$

On multiply by 6, both sides we get,

$\rm :\longmapsto\: - 18 < - 3 - 4x$

Adding 3 on both sides, we get

$\rm :\longmapsto\: - 18 + 3 < - 4x$

$\rm :\longmapsto\: - 15 < - 4x$

$\rm :\longmapsto\: - 4x > - 15$

On dividing by - 4, we get

$\bf\implies \:x < \dfrac{15}{4} - - - (1)$

Now, Consider

$\rm :\longmapsto\: - \dfrac{1}{2} - \dfrac{2x}{3} \leqslant \dfrac{5}{6}$

$\rm :\longmapsto\: \dfrac{ - 3 - 4x}{6} \leqslant \dfrac{5}{6}$

On multiply by 6 on both sides, we get

$\rm :\longmapsto\: - 3 - 4x \leqslant 5$

On adding 3, bothsides, we get

$\rm :\longmapsto\: - 4x \leqslant 5 + 3$

$\rm :\longmapsto\: - 4x \leqslant 8$

$\bf\implies \:x \geqslant - 2 - - - (2)$

From equation (1) and equation (2), we concluded that

$\rm :\longmapsto\: - 2 \leqslant x < \dfrac{15}{4}$

$\bf\implies \:x \: \in \: \bigg[ - 2, \: \dfrac{15}{4}\bigg)$

Additional Information :-

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

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

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

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

Answer 2

Step-by-step explanation:

$- 3 < \frac{ - 1}{2} - \frac{2x}{3} \leqslant \frac{5}{6} \\ - 3 < - \frac{(4x + 3)}{6} \leqslant \frac{5}{6} \\ - 18 < - 4x - 3 \leqslant 5 \\ - 15 < - 4x \leqslant 8 \\ - \frac{15}{4} < - x \leqslant 2 \\ \frac{15}{4} > x \geqslant - 2 \\ 3.75 > x \geqslant - 2$

I think u can complete the answer on ur own from here

good luck

Hope it helps :D