According to ques,
![\[~A\text{ }=\text{ }\{x\text{ }:\text{ }11x\text{ }\text{ }5\text{ }>\text{ }7x\text{ }+\text{ }3,\text{ }x\in R\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f8fa46dd1d9686d99969d28a1f5c7d2f_l3.png "Rendered by QuickLaTeX.com")
and
![\[B\text{ }=\text{ }\{x\text{ }:\text{ }18x\text{ }\text{ }9\text{ }\ge \text{ }15\text{ }+\text{ }12x,\text{ }x\in R\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1604c101eb2188fe60bad0f9433d2c1c_l3.png "Rendered by QuickLaTeX.com")
Solving for A,
![\[11x\text{ }\text{ }5\text{ }>\text{ }7x\text{ }+\text{ }3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-590e6b436dc94dff4365668574c5d223_l3.png "Rendered by QuickLaTeX.com")
![\[11x\text{ }\text{ }7x\text{ }>\text{ }3\text{ }+\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-656dc805311f45edd5f9e133e86c37af_l3.png "Rendered by QuickLaTeX.com")
![\[4x\text{ }>\text{ }8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f2b7f1f5e34e24a194b354495f98b9a6_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }>\text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3ab302e95380bfccba9fcfe91bcad600_l3.png "Rendered by QuickLaTeX.com")
Hence,
![\[~A\text{ }=\text{ }\{x\text{ }:\text{ }x\text{ }>\text{ }2,\text{ }x\in R\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d65f5d36cddb3cf710bfceb6c62eb0a0_l3.png "Rendered by QuickLaTeX.com")
Next, solving for B
![\[18x\text{ }\text{ }9\text{ }\ge \text{ }15\text{ }+\text{ }12x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-611a17d049c5eb865830c44312c1a7ed_l3.png "Rendered by QuickLaTeX.com")
![\[18x\text{ }\text{ }12x\text{ }\ge \text{ }15\text{ }+\text{ }9\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2e6c309e3152a853a2681cce318b146b_l3.png "Rendered by QuickLaTeX.com")
![\[6x\text{ }\ge \text{ }24\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-aff4044decd691655d7171f9c2ce826b_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }\ge \text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2d88e58afcb78e815a62b2dd774442d6_l3.png "Rendered by QuickLaTeX.com")
Hence,
![\[B\text{ }=\text{ }\{x\text{ }:\text{ }x\text{ }\ge \text{ }4,\text{ }x\in R\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-78bf3da8431b8fe031636219bbec1db9_l3.png "Rendered by QuickLaTeX.com")
Hence,
![\[A\text{ }\cap \text{ }B\text{ }=\text{ }x\text{ }\ge \text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-46965e9887d70a5d16c1e6f93d7a895f_l3.png "Rendered by QuickLaTeX.com")
Representing the solution on a number line:
According to ques,
and
Solving for A,
Hence,
Next, solving for B
Hence,
Hence,
Representing the solution on a number line:
