{"id":1659,"date":"2013-04-10T18:30:39","date_gmt":"2013-04-10T18:30:39","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=1659"},"modified":"2018-11-14T18:11:18","modified_gmt":"2018-11-14T18:11:18","slug":"math-inequalities-and-number-lines","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-inequalities-and-number-lines\/","title":{"rendered":"Math:  Inequalities and Number Lines"},"content":{"rendered":"<h1>As a math tutor, you&#8217;ll likely need to sort out a few basics about inequalities.<\/h1>\n<p>Generally, people prefer equations to inequalities. \u00a0Perhaps it&#8217;s for the reason that people like one definite answer to a problem: \u00a0for instance, &#8220;x=5&#8221;. \u00a0An inequality gives a set of valid answers, such as &#8220;x can be anything less than -1&#8221;. \u00a0I guess we&#8217;ll just have to get used to it:)<\/p>\n<p>More problematic &#8211; and more fixable &#8211; is that many people don&#8217;t know which sign is which. We can sort that out right now:<\/p>\n<p style=\"text-align: justify; padding-left: 210px;\"><span style=\"font-size: large;\">&lt; \u00a0 means less than<\/span><\/p>\n<p style=\"text-align: justify; padding-left: 210px;\"><span style=\"font-size: large;\">&gt; \u00a0 means greater than<\/span><\/p>\n<p>Some examples:<\/p>\n<p style=\"padding-left: 210px;\"><span style=\"font-size: large;\">10 &lt; 12<\/span><\/p>\n<p style=\"padding-left: 210px;\"><span style=\"font-size: large;\">20 &gt; 8<\/span><\/p>\n<p>Consider the number line:<br \/>\n<img decoding=\"async\" alt=\"\" src=\"\/numlin0.png\" \/><\/p>\n<p>Both less than and greater than actually refer to placement on the number line. \u00a0&#8220;Less than&#8221; means &#8220;to the left of&#8221;, while &#8220;greater than&#8221; means &#8220;to the right of&#8221;. \u00a0Of course, 10 is greater than 5, which is written 10 &gt; 5. \u00a0Notice that on the number line, 10 is to the right of 5.<\/p>\n<p>Similarly, 4 is less than 7. \u00a0In math, you write 4 &lt; 7. \u00a0Notice that on the number line, 4 is to the left of 7.<\/p>\n<p>It follows, of course, that -10 is less than -5. \u00a0After all, on the number line, -10 is to the left of -5. \u00a0Therefore,<\/p>\n<p style=\"padding-left: 210px;\"><span style=\"font-size: large;\">-10 &lt; -5<\/span><\/p>\n<p>People often have trouble with the idea that -10 &lt; -5. \u00a0They point out that 10 seems bigger than 5, so why would -10 be less than -5?<\/p>\n<p>The answer is that &#8220;less than&#8221; doesn&#8217;t refer to number size; it means &#8220;to the left of&#8221;. \u00a0On a number line, -10 is to the left of -5. \u00a0Therefore, -10 &lt; -5. \u00a0Similarly, 5 being to the left of 10, we write 5 &lt; 10.<\/p>\n<p>The practical issues of solving and graphing inequalites will be explored in future posts:)<\/p>\n<p>Jack of <a href=\"..\/\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>As a math tutor, you&#8217;ll likely need to sort out a few basics about inequalities. Generally, people prefer equations to inequalities. \u00a0Perhaps it&#8217;s for the reason that people like one definite answer to a problem: \u00a0for instance, &#8220;x=5&#8221;. \u00a0An inequality &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-inequalities-and-number-lines\/\"> <span class=\"screen-reader-text\">Math:  Inequalities and Number Lines<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1659","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1659","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=1659"}],"version-history":[{"count":31,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1659\/revisions"}],"predecessor-version":[{"id":36189,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1659\/revisions\/36189"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=1659"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=1659"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=1659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}