Solution:
From the question it is given that,
![\[3x-7>5x-1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-37fcf2d16b704b24edd5651a994b199a_l3.png "Rendered by QuickLaTeX.com")
Add
![\[7\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6064bfa4cc3ec5261b106372b5e270dd_l3.png "Rendered by QuickLaTeX.com")
to both the sides, we get
![\[3x>5x+6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b63315ba78b8e0e92e69b0431fe943f9_l3.png "Rendered by QuickLaTeX.com")
Again, subtract
![\[5x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a9a95c543d6859a1f3489a29b9ae0493_l3.png "Rendered by QuickLaTeX.com")
from both the sides,
![\[-2x>6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6c3dad55529e0366f7bba196c1defe5e_l3.png "Rendered by QuickLaTeX.com")
Divide both sides by
![\[-2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e9d08fbe629fe6b5dfacd369fab215e0_l3.png "Rendered by QuickLaTeX.com")
we get
![\[x<-3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-99902b8b24763c6bcf308fd6b8d6b9b1_l3.png "Rendered by QuickLaTeX.com")
The solutions of
inequality are defined by all the real numbers less than
![\[-3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4adc8c45b73d97c997db1b8d065f32a8_l3.png "Rendered by QuickLaTeX.com")
.
Therefore, the required solution set is
![\[(-\infty ,-3)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-02dbbe3e9f37958ce2f7cfb352077e38_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d32e615a6517b76e65b04fd25ae8bf0a_l3.png "Rendered by QuickLaTeX.com")
, and 
.