<p>A linear inequality compares expressions that are linear in the unknown, using <, >, ≤ or ≥. It is a relation, not a function.</p>
<p>The symbols of inequality are</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 500px;"><colgroup><col style="width: 60.0000%;"><col style="width: 40.0000%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>Meaning</p></th><th style="text-align: center; --cell-justify: center"><p>Other phrase(s) used</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>o&nbsp;&nbsp; ‘&lt;’ means ‘is less than’</p></td><td style="text-align: center; --cell-justify: center"><p>o&nbsp;&nbsp; smaller than</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>o&nbsp;&nbsp; ‘&gt;’ means ‘is more than’</p></td><td style="text-align: center; --cell-justify: center"><p>o&nbsp;&nbsp; greater than</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>‘≤’ means ‘is less than or equal to’</p></td><td style="text-align: center; --cell-justify: center"><p>o&nbsp;&nbsp; at most</p><p>o&nbsp;&nbsp; not more than</p><p>o&nbsp;&nbsp; greatest (largest) possible</p><p>o&nbsp;&nbsp; maximum</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>‘≥’ means ‘is greater than or equal to’</p></td><td style="text-align: center; --cell-justify: center"><p>o&nbsp;&nbsp; at least</p><p>o&nbsp;&nbsp; not less than</p><p>o&nbsp;&nbsp; least (smallest) possible</p><p>o&nbsp;&nbsp; minimum</p></td></tr></tbody></table></div></div>
<p style="margin-top: 1.5rem">The following are the some example on how to represent the different inequalities on a number line</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 600px;"><colgroup><col style="width: 16.6667%;"><col style="width: 83.3333%;"></colgroup><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>(a) \(x&gt;1\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765522688762-p7cmu6y92dm.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU1MjI2ODg3NjItcDdjbXU2eTkyZG0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzAxMjA3OCwiZXhwIjoxNzkzMDEyMzc4fQ.8zFWeJW_d1d1xOIoWaH6-vShwmETG910scF_0ICOD8Q" data-width="50%" style="width: 50%; max-width: 50%;"></p></th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>(b) \(x\le -9\)</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765522724979-na2htz44cdq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU1MjI3MjQ5NzktbmEyaHR6NDRjZHEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzAxMjA3OCwiZXhwIjoxNzkzMDEyMzc4fQ.p405hR2BxJA4UghGtczkxDQhyIjVVCltG1AoO7kriF4" data-width="50%" style="width: 50%; max-width: 50%;"></p></td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>(c) \(0\le x&lt;4\)</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765522737740-1ijacx5q6r9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU1MjI3Mzc3NDAtMWlqYWN4NXE2cjkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzAxMjA3OCwiZXhwIjoxNzkzMDEyMzc4fQ.1frRCG00XSCfWZNtR-uhIQndUw7QM-n_63fvbl2Mr4o" data-width="50%" style="width: 50%; max-width: 50%;"></p></td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>(d) \(3\ge x\ge -2\)</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765522748914-9maejj85gzf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU1MjI3NDg5MTQtOW1hZWpqODVnemYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzAxMjA3OCwiZXhwIjoxNzkzMDEyMzc4fQ.ImLcBKRwLbKCi6XJSolteR348iG1FsycWtXqJ6_mxv4" data-width="50%" style="width: 50%; max-width: 50%;"></p></td></tr></tbody></table></div></div>

A linear inequality compares expressions that are linear in the unknown, using <, >, ≤ or ≥. It is a relation, not a function.

The following are the some example on how to represent the different inequalities on a number line

Meaning	Other phrase(s) used
o ‘<’ means ‘is less than’	o smaller than
o ‘>’ means ‘is more than’	o greater than
‘≤’ means ‘is less than or equal to’	o at most o not more than o greatest (largest) possible o maximum
‘≥’ means ‘is greater than or equal to’	o at least o not less than o least (smallest) possible o minimum

Linear Inequality

Linear Inequality

Video Solution:

Solution:

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(a) \(x>1\)
(b) \(x\le -9\)
(c) \(0\le x<4\)
(d) \(3\ge x\ge -2\)