document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91076>Question 91076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve 8x-5+9x=17x-5. Describe the type of answer if applicable </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66696 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=66696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "8x - 5 + 9x = 17x - 5<BR>\n" );
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document.write( "Notice that on the left side you can combine the two terms that contain x. 8x + 9x equals 17x.<BR>\n" );
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document.write( "When you make that change the equation becomes:<BR>\n" );
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document.write( "17x - 5 = 17x - 5<BR>\n" );
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document.write( "Notice that the left side of this equation is identical to the right side.  Because of<BR>\n" );
document.write( "this reason, this type of equation is called an identity.  Whatever value you wish to choose<BR>\n" );
document.write( "for x, the given equation will always be true.  <BR>\n" );
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document.write( "For example, in the given equation if you substitute 10 for x the equation becomes:<BR>\n" );
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document.write( "8(10) - 5 + 9(10) = 17(10) - 5<BR>\n" );
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document.write( "and this simplifies to:<BR>\n" );
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document.write( "80 - 5 + 90 = 170 - 5<BR>\n" );
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document.write( "which further reduces to:<BR>\n" );
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document.write( "165 = 165<BR>\n" );
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document.write( "Now try a different value for x. Suppose you choose x = 0. The equation becomes:<BR>\n" );
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document.write( "8(0) - 5 + 9(0) = 17(0) - 5<BR>\n" );
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document.write( "and this reduces to:<BR>\n" );
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document.write( "-5 = -5<BR>\n" );
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document.write( "Finally, let's choose x = -4. Substituting this value for x in the given equation <BR>\n" );
document.write( "gives:<BR>\n" );
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document.write( "8(-4) - 5 + 9(-4) = 17(-4) - 5<BR>\n" );
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document.write( "Doing the multiplications results in:<BR>\n" );
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document.write( "-32 - 5 - 36 = -68 - 5<BR>\n" );
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document.write( "and combining the terms on the left and right sides:<BR>\n" );
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document.write( "-73 = -73<BR>\n" );
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document.write( "This should give you the idea of what an identity means. Our examples show that no matter<BR>\n" );
document.write( "what value we tried for x, both sides of the given equation were equal.  <BR>\n" );
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document.write( "Hope this clarifies the problem for you. </SPAN>\n" );
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