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Linear Inequalities

Short Answer Type

51.

Solve the following inequality and show the solution graphically on the number line:

$fraction numerator 4 straight x over denominator 3 end fraction minus 9 over 4 less or equal than straight x plus 3 over 4. space space space open parentheses fraction numerator 7 straight x minus 1 over denominator 3 end fraction close parentheses minus open parentheses fraction numerator 7 straight x plus 2 over denominator 6 end fraction close parentheses greater or equal than straight x$

152 Views

52.

Solve the following inequality and show the solution graphically on the number line:

$2 space left parenthesis 2 straight x plus 3 right parenthesis space minus space 10 space less than space 6 space left parenthesis straight x space minus space 2 right parenthesis semicolon space space open parentheses fraction numerator straight x minus 2 over denominator 2 end fraction close parentheses plus 13 greater or equal than 2 plus fraction numerator 4 straight x over denominator 3 end fraction$

143 Views

53.

Solve the following inequality and show the solution graphically on the number line.

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

179 Views

54.

Solve the following inequality and show the solution graphically on the number line.

$4 minus 5 straight x greater than negative 11 semicolon space 4 straight x plus 11 less or equal than negative 3$

159 Views

55.

Solve the following inequality and show the solution graphically on the number line.

$7 straight x minus 8 space less than space 4 straight x plus 7 semicolon space minus straight x over 2 greater than 4$

165 Views

56.

Solve the following inequality and show the solution graphically on the number line.

$space space 5 straight x minus 7 less than 3 space left parenthesis straight x plus 3 right parenthesis semicolon space 1 minus fraction numerator 3 straight x over denominator 2 end fraction greater or equal than straight x minus 4$

175 Views

57.

Solve the following inequality and show the solution graphically on the number line:

$2 less or equal than 3 straight x minus 4 less or equal than 5$

149 Views

58.

Solve the following inequality and show the solution graphically on the number line:

$7 less than 4 minus fraction numerator 3 straight x over denominator negative 5 end fraction less or equal than 10$

267 Views

59.
Solve the following inequality for (i) $straight x space element of space straight N comma$ (ii) $space space space space straight x space element of space straight Z comma$ (iii) $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ and show that the graphs of the solutions on the number line. : 3x - 2 < 2x + 1

3x - 2 < 2x + 1 $rightwards double arrow$ 3x - 2x < 1 + 2 $rightwards double arrow$ x < 3

(i) Solution for $straight x space element of space straight N space rightwards double arrow space straight x space equals space 1 comma space 2$

The solution set is $open curly brackets 1 comma space 2 close curly brackets.$ The graph on the number line is:

(ii) $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

$rightwards double arrow$ x = 2, 1, 0, -1, -2, -3, ............

∴ The solution set is $open curly brackets..... comma space minus 3 comma space minus 2 comma space minus 1 comma space 0 comma space 1 comma space 2 close curly brackets.$ The graph on the number line is:

(iii) $straight x less than 3 comma space straight x space element of space straight R space rightwards double arrow space straight x space element of space left parenthesis negative infinity comma space 3 right parenthesis.$ The graph on the number line is:

105 Views

60.

Solve the following inequality for (i) $straight x space element of space straight N comma$ (ii) $space space space space straight x space element of space straight Z comma$ (iii) $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ and show that the
graphs of the solutions on the number line. : $5 straight x minus 3 greater or equal than 3 straight x minus 5.$