{"id":1099,"date":"2013-07-31T04:20:01","date_gmt":"2013-07-31T04:20:01","guid":{"rendered":"?page_id=1099"},"modified":"2013-07-31T04:20:01","modified_gmt":"2013-07-31T04:20:01","slug":"page-102","status":"publish","type":"page","link":"https:\/\/www.collegeprepalgebra.com\/cpa\/content\/math-help\/chapter-3\/section-1\/page-102\/","title":{"rendered":"Page 102"},"content":{"rendered":"
\n

Math Help for Section 3.1, Page 102<\/h2>\n<\/h2>\n

\nSolving
\nLinear Equations in Standard Form <\/span>
\nIn the first two chapters, you were introduced to the rules of algebra,
\nand you learned to use these rules to rewrite and simplify algebraic
\nexpressions. In Sections 2.3 and 2.4, you gained experience in
\ntranslating verbal phrases and problems into algebraic expressions and
\nequations. You are now ready to use these skills and experiences to
\nsolve linear equations
\nin one variable<\/span>.<\/p>\n

    A linear equation in one
\nvariable is also called a first-degree
\nequation<\/span> because its variable has an implied exponent of
\n1 $\\left( {x = {x^1}} \\right).$ Here are
\nsome examples of linear equations in standard form. <\/p>\n\n\n\n\n\n
$2x = 0$<\/td>\n$4x + 6 = 0$<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/tr>\n
$x – 7 = 0$<\/td>\n$\\displaystyle{x \\over 2} – 1 = 0$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Remember that to solve<\/span>
\nan equation involving x<\/span>
\nmeans to find
\nall values of x<\/span>
\nthat satisfy the equation. For the linear equation $ax + b = 0,$ the
\ngoal is to isolate x<\/span>
\nby rewriting the equation in the form\n<\/p>\n

    \"\"  
\n     Isolate
\nthe variable x<\/span>.<\/small><\/p>\n

To obtain this form, you use the techniques discussed in
\nSection 2.4. That is, you begin with the original equation and use the
\nProperties of Equality from page 88 to eliminate terms or factors until
\nyou isolate the variable. For instance, to solve the linear equation $x
\n– 2 = 5,$
\nyou can add 2 to each side of the equation to obtain $x = 7.$ As
\nmentioned in
\nSection 2.4, each equivalent equation is called a step of the
\nsolution. \n<\/p>\n

Example
\n1: Tip<\/span>
\n
\nSolving an equation has two basic stages. The first stage is to find<\/span>
\nthe solution (or solutions). The second stage is to check<\/span> that each
\nsolution satisfies the original equation. You can
\nimprove your accuracy in algebra by developing the habit of checking
\neach solution. <\/p>\n

\nWhile completing the first stage, a common question in algebra is\n<\/p>\n

“How do I know what to do
\nfirst<\/span> to
\nisolate x<\/span>?”\n<\/div>\n

The answer is that you need practice. By solving many linear
\nequations, you will find that your skill will improve. The key thing to
\nremember is that you can “get rid of” terms and factors by using inverse<\/span> operations.
\nHere are some guidelines and examples.\n<\/p>\n\n\n\n\n\n\n\n
    Guideline <\/td>\n Equation <\/td>\n<\/td>\n    Inverse Operation <\/td>\n<\/tr>\n
Subtract
\nto remove a sum. <\/span><\/td>\n		$x + 3 = 0$<\/td>\n   <\/td>\nSubtract
\n3 from each side.<\/span><\/td>\n<\/tr>\n
Add
\nto remove a difference. <\/span><\/td>\n		$x – 5 = 0$<\/td>\n<\/td>\nAdd
\n5 to each side.<\/span><\/td>\n<\/tr>\n
Divide
\nto remove a product. <\/span><\/td>\n		$4x = 20$<\/td>\n<\/td>\nDivide
\neach side by 4.<\/span><\/td>\n<\/tr>\n
Multiply
\nto remove a quotient. <\/span><\/td>\n		$\\displaystyle{x \\over 8} = 0$<\/td>\n<\/td>\nMultiply
\neach side by 8.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\nHere is how you could use this technique in Example 1.\n<\/p>\n\n\n\n\n\n
    Guideline <\/td>\n Equation <\/td>\n<\/td>\n    Inverse Operation <\/td>\n<\/tr>\n
Add to remove a difference. <\/span><\/td>\n$3x – 15 = 0$<\/td>\n   <\/td>\nAdd 15 to each side.<\/span><\/td>\n<\/tr>\n
Divide to remove a product. <\/span><\/td>\n$3x = 15$<\/td>\n<\/td>\nDivide each side by 3.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

For additional examples, review Example 4 on page 89. Note how inverse operations are used to isolate
\nthe variable.\n<\/p>\n<\/div>\n


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Math Help for Section 3.1, Page 102 Solving Linear Equations in Standard Form In the first two chapters, you were introduced to the rules of algebra, and you learned to use these rules to rewrite and simplify algebraic expressions. In … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":851,"menu_order":510,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1099","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/1099","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=1099"}],"version-history":[{"count":0,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/1099\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/851"}],"wp:attachment":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/media?parent=1099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}