Solve the following inequality for real x: from Mathematics Lin
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    Linear Inequalities

    Multiple Choice QuestionsShort Answer Type

    1. Solve 24x < 100, when

    (i) x is a natural number

    (ii) x is an integer
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    2.

    Solve -12x > 30, when

    (i) x is a natural number.            (ii) x is an integer.

    452 Views
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    3.

    Solve 5x – 3 < 7, when

    (i) x is an integer.              (ii) x is a real number.          

    474 Views
    Answer
    4.

    Solve 3x + 8 > 2, when

    (i) x is an integer.              (ii) x is a real number.          

    600 Views
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    5. Solve the following inequality for real x:

    3(x – 1) ≤ 2 (x – 3)
    398 Views
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    6. Solve the following inequality for real x:

    3 (2 – x) ≥ 2 (1 – x)
    109 Views
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    7. Solve the following inequality for real x:

    fraction numerator 3 space left parenthesis straight x minus 2 right parenthesis over denominator 5 end fraction less or equal than fraction numerator 5 space left parenthesis 2 straight x minus 3 right parenthesis over denominator 3 end fraction
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    8. Solve the following inequality for real x:

    1 half open parentheses fraction numerator 3 straight x over denominator 5 end fraction plus 4 close parentheses greater or equal than 1 third left parenthesis straight x minus 6 right parenthesis
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    9. Solve the following inequality for real x:

    <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>

    <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>

    Multiply by L.C.M. 60 of 4, 3 and 5, we have

    rightwards double arrow           space space 15 straight x less than space 20 space left parenthesis 5 straight x minus 2 right parenthesis minus 12 space left parenthesis 7 straight x minus 3 right parenthesis space rightwards double arrow space 15 straight x space less than space 100 straight x minus 40 minus 84 straight x plus 36

    rightwards double arrow    15x - 100x + 84x < - 40 + 36 rightwards double arrow -x < -4 rightwards double arrow x > 4                      (Divide by -1)

    rightwards double arrow                         straight x space element of space left parenthesis 4 comma space infinity right parenthesis

    Hence, the solution set is <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>



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    10. Solve the following inequality for real x:

    fraction numerator left parenthesis 2 straight x minus 1 right parenthesis over denominator 3 end fraction greater or equal than fraction numerator left parenthesis 3 straight x minus 2 right parenthesis over denominator 4 end fraction minus fraction numerator left parenthesis 2 minus straight x right parenthesis over denominator 5 end fraction
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