{"id":1136,"date":"2013-07-31T04:20:01","date_gmt":"2013-07-31T04:20:01","guid":{"rendered":"?page_id=1136"},"modified":"2013-07-31T04:20:01","modified_gmt":"2013-07-31T04:20:01","slug":"page-146","status":"publish","type":"page","link":"https:\/\/www.collegeprepalgebra.com\/cpa\/content\/math-help\/chapter-3\/section-6\/page-146\/","title":{"rendered":"Page 146"},"content":{"rendered":"
\n

Math Help for Section 3.6, Page 146<\/h2>\n<\/h2>\n

\nSolving Linear Inequalities<\/span>
An inequality in one variable is a linear inequality<\/span> if it can be written in one of
\nthe following forms.\n<\/p>\n

    $ax+b\\le0$,    $ax+b<0$,    $ax+b\\ge0$,    $ax+b>0$<\/p>\n

    Solving a linear inequality is much like solving a linear equation. You
\nisolate the
\nvariable by using the properties
\nof inequalities<\/span>. These properties are similar to
\nthe properties of equality, but there are two important exceptions. When each
\nside of an inequality is multiplied or divided by a negative number,
\nthe direction
\nof the inequality symbol must be reversed<\/span>. Here is an
\nexample.\n<\/p>\n

    $\\eqalign{-2<&5
\n&{\\small\\color{red}\\quad\\quad\\text{Original inequality}} \\cr
\n{\\color{red}(-3)}(-2)>&{\\color{red}(-3)}(5)
\n&{\\small\\color{red}\\quad\\quad\\text{Multiply each side by
\n}-3\\text{ and reverse the inequality.}}
\n\\cr 6>&-15
\n&{\\small\\color{red}\\quad\\quad\\text{Simplify.}} }$<\/p>\n

    Two inequalities that have the same solution set are equivalent inequalities<\/span>.
\nThe list of operations on page 80 can be used to create equivalent
\ninequalities. These properties remain true when the symbols $<$ and
\n$>$ are replaced by $\\le$ and $\\ge$.
\nMoreover, a<\/span>,
\nb<\/span>, and c<\/span> can represent
\nreal numbers, variables, or expressions. Note
\nthat you cannot multiply or divide each side of an inequality by zero.\n<\/p>\n

\nStudy Tip<\/span>
\nThe solution set of a linear inequality can be written in set notation<\/span>. For instance, the
\nsolution $x>1$ is written in set notation as $\\{x|x>1\\}$ and is
\nread “the set of all x<\/span>
\nsuch that x<\/span>
\nis greater than 1.”\n<\/p>\n

Example 3: Tip<\/span>
The solution set in set notation is $\\{x|x<3\\}$.\n<\/p>\n<\/p>\n<\/div>\n


\n
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Math Help for Section 3.6, Page 146 Solving Linear InequalitiesAn inequality in one variable is a linear inequality if it can be written in one of the following forms.     $ax+b\\le0$,    $ax+b<0$,    $ax+b\\ge0$,    $ax+b>0$     Solving a linear inequality is … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":891,"menu_order":730,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1136","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/1136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/comments?post=1136"}],"version-history":[{"count":0,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/1136\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/891"}],"wp:attachment":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/media?parent=1136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}