Question

solve it please on copy​

Answer 1

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

Given inequality is

$\rm :\longmapsto\:15x - 6 < 17x + 4 \leqslant 5x + 10$

Now,

Consider,

$\rm :\longmapsto\:15x - 6 < 17x + 4$

On Subtracting 17x from both sides,

$\rm :\longmapsto\:15x - 17x - 6 <17x - 17x + 4$

$\rm :\longmapsto\: - 2x - 6 < 4$

On adding 6 on both sides, we get

$\rm :\longmapsto\: - 2x - 6 + 6< 4 + 6$

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

On dividing by - 2, we get

$\bf\implies \:x > - \: 5 - - - (1)$

Consider,

$\rm :\longmapsto\:17x + 4 \leqslant 5x + 10$

On Subtracting 5x from both sides,

$\rm :\longmapsto\:17x + 4 - 5x\leqslant 5x + 10 - 5x$

$\rm :\longmapsto\:12x + 4 \leqslant10$

On Subtracting 4 from both sides, we get

$\rm :\longmapsto\:12x + 4 - 4\leqslant10 - 4$

$\rm :\longmapsto\:12x \leqslant 6$

$\bf\implies \:x \leqslant \dfrac{1}{2} - - - (2)$

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

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

$\bf\implies \:x \: \in \: ( - 5, \dfrac{1}{2} \bigg]$

Additional Information :-

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

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

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

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

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

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

$\boxed{ \sf{ \: xy > 0\: \implies \:x > 0 \: and \: y > 0 \: \: or \: x < 0 \: and \: y < 0}}$

$\boxed{ \sf{ \: xy < 0\: \implies \:x > 0 \: and \: y < 0 \: \: or \: x < 0 \: and \: y > 0}}$