![\[\begin{array}{*{35}{l}} \left( 2x\text{ }+\text{ }3 \right)/4\text{ }-\text{ }3\text{ }<\text{ }\left( x\text{ }-\text{ }4 \right)/3\text{ }-\text{ }2 \\ \left( 2x\text{ }+\text{ }3 \right)/4\text{ }-\text{ }3\text{ }+\text{ }3\text{ }<\text{ }\left( x\text{ }-\text{ }4 \right)/3\text{ }-\text{ }2\text{ }+\text{ }3 \\ \left( 2x\text{ }+\text{ }3 \right)/4\text{ }<\text{ }\left( x\text{ }-\text{ }4 \right)/3\text{ }+\text{ }1 \\ \left( 2x\text{ }+\text{ }3 \right)/4\text{ }<\text{ }\left( x\text{ }-\text{ }4\text{ }+\text{ }3 \right)/3 \\ \left( 2x\text{ }+\text{ }3 \right)/4\text{ }<\text{ }\left( x\text{ }-\text{ }1 \right)/3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4e3e21b3ad8fbbfa929e321c7ca03f49_l3.png "Rendered by QuickLaTeX.com")
Cross multiplying we get,
![\[\begin{array}{*{35}{l}} 3\text{ }\left( 2x\text{ }+\text{ }3 \right)\text{ }<\text{ }4\text{ }\left( x\text{ }-\text{ }1 \right) \\ 6x\text{ }+\text{ }9\text{ }<\text{ }4x\text{ }-\text{ }4 \\ 6x\text{ }+\text{ }9\text{ }-\text{ }9\text{ }<\text{ }4x\text{ }-\text{ }4\text{ }-\text{ }9 \\ 6x\text{ }<\text{ }4x\text{ }-\text{ }13 \\ 6x\text{ }-\text{ }4x\text{ }<\text{ }4x\text{ }-\text{ }13\text{ }-\text{ }4x \\ 2x\text{ }<\text{ }-13 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-47ccc8f334ff1d4206cd40f71e7d8b46_l3.png "Rendered by QuickLaTeX.com")
Divide both sides by 2, we get
![\[\begin{array}{*{35}{l}} 2x/2\text{ }<\text{ }-13/2 \\ x\text{ }<\text{ }-13/2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7101fb59fa525daa11d5f22652f7888d_l3.png "Rendered by QuickLaTeX.com")
∴ The solution of the given inequation is (-∞, -13/2).
Cross multiplying we get,
Divide both sides by 2, we get
∴ The solution of the given inequation is (-∞, -13/2).