{"id":1032,"date":"2013-07-31T04:03:35","date_gmt":"2013-07-31T04:03:35","guid":{"rendered":"?page_id=1032"},"modified":"2013-07-31T04:03:35","modified_gmt":"2013-07-31T04:03:35","slug":"page-6","status":"publish","type":"page","link":"https:\/\/www.algebrawithinreach.com\/eia6e\/content\/math-help\/chapter-1\/section-1\/page-6\/","title":{"rendered":"Page 6"},"content":{"rendered":"
\n

Math Help for Section 1.1, Page 6<\/h2>\n<\/h2>\n

Absolute
\nValue <\/span>
\n
\nThe figures below illustrate the concept of opposites with the real
\nnumber line.<\/p>\n

\"\"<\/div>\n

\nParentheses are useful for denoting the opposite of a negative number.
\nFor example, $ -\\left({ -3}\\right)$ means the opposite of $-3$ which
\nis 3. That is,
\n\n<\/p>\n

<\/p>\n\n\n\n
   $ -\\left( {-3} \\right) = 3.$<\/td>\nThe opposite of
\n$ -3$ is 3.<\/small><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/p>\n

   
\nBecause opposite numbers lie
\nthe same distance from zero on the real
\nnumber line, they have the same absolute value. So, $\\left| {5}
\n\\right| = 5$ and $\\left| {-5} \\right| = 5$ (see figure
\nbelow).\n<\/p>\n

\"\"<\/div>\n

You can write this more simply as $\\left| {5} \\right| =
\n\\left| {-5} \\right| = 5.$ <\/p>\n

   
\nAnother way to define absolute
\nvalue is as follows.  If a<\/span>
\nis a
\nreal number, then the absolute
\nvalue<\/span> of a<\/span>
\nis <\/p>\n


\n    $\\left| a \\right| = \\begin{cases} a
\n& \\text{ if } a\\ge 0 \\\\
\n-a & \\text{ if } a \\lt 0
\n\\end{cases}$
\n<\/p>\n

   
\nThe definition says that the
\nabsolute value of a nonnegative number is
\nthat number and that the absolute value of a negative number is the
\nopposite of that number. So, the absolute value of a real number is
\neither positive or zero (never negative). Note that zero is the only
\nreal number whose absolute value is 0. That is, $\\left| {\\,0\\,} \\right|
\n= 0.$ <\/p>\n

   
\nThe word expression<\/span>
\nmeans a
\ncollection of numbers and symbols such as $3 + 5$
\nor $\\left| {-4} \\right|.$ When asked to evaluate<\/span> an
\nexpression,
\nyou are to find the number
\nthat is equal to the expression. For instance, $3 + 5 = 8$ and $\\left|
\n{-4} \\right| = 4.$ <\/p>\n

<\/p>\n

Example
\n5: Tip<\/span>
\n
\nNote in Example 5(d) that $-\\left| {-6} \\right| =-6$ does not
\ncontradict the fact that the
\nabsolute value of a real number cannot be negative. The expression $ –
\n\\,\\left| {-6} \\right|$
\ncalls for the opposite of an absolute value (the opposite of a positive
\nnumber), so it must be negative. <\/p>\n<\/div>\n

<\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"

Math Help for Section 1.1, Page 6 Absolute Value The figures below illustrate the concept of opposites with the real number line. Parentheses are useful for denoting the opposite of a negative number. For example, $ -\\left({ -3}\\right)$ means the … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":763,"menu_order":30,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1032","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/pages\/1032","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/comments?post=1032"}],"version-history":[{"count":0,"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/pages\/1032\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/pages\/763"}],"wp:attachment":[{"href":"https:\/\/www.algebrawithinreach.com\/eia6e\/wp-json\/wp\/v2\/media?parent=1032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}