Number line & inequalities

<p>In some cases, an unknown $x$ has to satisfy two or more linear inequalities simultaneously. </p>
<p>Then the solution will be the <strong>common solution</strong> to all the simultaneous linear inequalities. </p>
<p>Let’s try to find the common solution for the following pairs of inequalities by first representing each inequality on the same number line and then find the overlapping region. </p>
<ol class="abc-list"><li><div class="list-item-paragraph">$x>2$ and $x\le 4$</div><div class="list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765530832114-hch72ugasg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU1MzA4MzIxMTQtaGNoNzJ1Z2FzZy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzMDExMDU0LCJleHAiOjE3OTMwMTEzNTR9.q9YfnludnQF7hTlpMs7XISm6kecerpp0qkjatFg8tpg" alt="List item image" class="aligncenter custom-width" style="max-width: 400px; height: auto;" /></div></li><li><div class="list-item-paragraph">$x<-1$ and $x\le 2$</div><div class="list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765530882817-thw7lf04qss.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU1MzA4ODI4MTctdGh3N2xmMDRxc3MucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzAxMTA1NCwiZXhwIjoxNzkzMDExMzU0fQ.AT1uSNAk2NlWXhZVAaJaBcj9GO-uz2_QAPTsRFkut1w" alt="List item image" class="aligncenter custom-width" style="max-width: 400px; height: auto;" /></div><div class="list-item-paragraph" style="text-align: center">Solution: $x<-1$</div></li></ol>
<p>The inequalities that represent the overlapping region is the common solution.</p>

In some cases, an unknown $x$ has to satisfy two or more linear inequalities simultaneously. 

Then the solution will be the **common solution** to all the simultaneous linear inequalities. 

Let’s try to find the common solution for the following pairs of inequalities by first representing each inequality on the same number line and then find the overlapping region. 

Common Solution

Common Solution

Video Solution:

Solution:

Solution locked