Question

please gives answerrrrrrr asap​

Answer 1

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

Given inequality is

$\rm :\longmapsto\: - 5 \leqslant \dfrac{2x}{5} + 1 < - 1 \: \: where \: x \: \in \: N$

can be rewritten as

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

On multiply by 5, each term we get

$\rm :\longmapsto\: - 25 \leqslant 2x + 5 < - 5$

On Subtracting 5, from each term, we get

$\rm :\longmapsto\: - 25 - 5 \leqslant 2x + 5 - 5< - 5 - 5$

$\rm :\longmapsto\: - 30 \leqslant 2x< - 10$

On dividing by 2, each term we get

$\rm :\longmapsto\: - 15 \leqslant x< - 5$

$\bf\implies \:x \: \in \: [ - 15, \: - 5)$

As x is a natural number,

So, there is no solution.

Additional Information :-

Let take one more example of same type!!!

Question :- Solve the following inequality

$\rm :\longmapsto\: - 5 \leqslant \dfrac{2x}{5} + 1 < 3 \: \: where \: x \: \in \: N$

Solution :-

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

On multiply by 5, each term we get

$\rm :\longmapsto\: - 25 \leqslant 2x + 5 < 15$

On Subtracting 5 from each term, we get

$\rm :\longmapsto\: - 25 - 5\leqslant 2x + 5 - 5 < 15 - 5$

$\rm :\longmapsto\: - 30\leqslant 2x < 10$

On dividing each term by 2, we get

$\rm :\longmapsto\: - 15\leqslant x < 5$

As x is a natural number,

So,

$\bf\implies \:x \: = \: \{1,2,3,4 \}$

More about inequalities

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

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

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

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