Question

solve the following in equation and write the solution set .also represent it one the number of line (13x-5 < 15x + 4 < 7x +12 ,XER​

Answer 1

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

The given inequality is

$\rm :\longmapsto\:13x - 5 < 15x + 4 < 7x + 12$

Let we consider,

$\rm :\longmapsto\:13x - 5 < 15x + 4$

On adding 5, on both sides,

$\rm :\longmapsto\:13x - 5 + 5 < 15x + 4 + 5$

$\rm :\longmapsto\:13x < 15x + 9$

On Subtracting 15x, on both sides

$\rm :\longmapsto\:13x - 15x < 15x + 9 - 15x$

$\rm :\longmapsto\: - 2x < 9$

$\bf\implies \:x > - \: \dfrac{9}{2} - - - - - (1)$

Now, Let we consider,

$\rm :\longmapsto\:15x + 4 < 7x + 12$

On Subtracting 7x, from both sides

$\rm :\longmapsto\:15x + 4 - 7x < 7x + 12 - 7x$

$\rm :\longmapsto\:8x + 4 < 12$

On Subtracting 4, from both sides,

$\rm :\longmapsto\:8x + 4 - 4< 12 - 4$

$\rm :\longmapsto\:8x < 8$

$\bf\implies \:x < 1 - - - - - (2)$

Now, Combine equation (1) and equation (2),

$\bf :\longmapsto\: - \: \dfrac{9}{2} < x < 1$

$\bf\implies \:x \: \in \: \bigg( - \: \dfrac{9}{2}, \: 1 \bigg)$

Answer 2

Answer:

*6"?'665*4,66=6=7=65

Step-by-step explanation:

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