Binomial Theorem

Question
CBSEENMA11014366

Solve the following inequality:

space space minus 15 less than fraction numerator 3 left parenthesis straight x minus 2 right parenthesis over denominator 5 end fraction less or equal than 0




















Solution

space space minus 15 less than fraction numerator 3 left parenthesis straight x minus 2 right parenthesis over denominator 5 end fraction less or equal than 0
Now,    negative 15 less than fraction numerator 3 space left parenthesis straight x minus 2 right parenthesis over denominator 5 end fraction rightwards double arrow space minus 75 less than 3 space left parenthesis straight x minus 2 right parenthesis space rightwards double arrow negative 75 space less than space 3 straight x minus 6 rightwards double arrow space minus 3 straight x less than negative 6 plus 75


rightwards double arrow                -3x < 69         rightwards double arrow space space space space space space space space fraction numerator negative 3 straight x over denominator negative 3 end fraction greater than fraction numerator 69 over denominator negative 3 end fraction                  (∵ -3 < 0)
rightwards double arrow                  x > -23                                                                                                   ...(i)
Also,             <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>     ...(ii)
From (i) and (ii), we have -23 < x less or equal than 2 which is the required solution of the given inequality.
Hence, the solution set is (-23, 2].

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