document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85687>Question 85687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Combining the Rules to Solve Equations<BR>\n" );
document.write( "Solve for x and check your result<BR>\n" );
document.write( "9x + 7 = 5x - 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61931 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=61931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9x + 7 = 5x - 3<BR>\n" );
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document.write( "The goals in this problem will be to:<BR>\n" );
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document.write( "1) collect all the terms containing x on one side of the equation (by using subtraction)<BR>\n" );
document.write( "2) collect all the numbers on the other side of the equation (by using subtraction)<BR>\n" );
document.write( "3) combine terms on both sides of the equation (by adding them)<BR>\n" );
document.write( "4) solve for x by dividing both sides of the equation by the multiplier of x<BR>\n" );
document.write( "5) check by substituting the value of x into the original equation to make sure both sides<BR>\n" );
document.write( "are equal.<BR>\n" );
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document.write( "Step 1):<BR>\n" );
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document.write( "Get rid of the 5x on the right side by subtracting 5x from both sides to get:<BR>\n" );
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document.write( "9x -5x + 7 = -3<BR>\n" );
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document.write( "Step 2):<BR>\n" );
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document.write( "Get rid of the + 7 on the left side by subtracting +7 from both sides:<BR>\n" );
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document.write( "9x - 5x = -3 - 7<BR>\n" );
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document.write( "Step 3):<BR>\n" );
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document.write( "Combine the terms on both sides and this results in:<BR>\n" );
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document.write( "4x = -10<BR>\n" );
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document.write( "Step 4):<BR>\n" );
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document.write( "Solve for x by dividing both sides by the multiplier of x (multiplier = 4):<BR>\n" );
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document.write( "4x/4 = -10/4<BR>\n" );
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document.write( "and this reduces to:<BR>\n" );
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document.write( "x = -10/4 = -5/2 <BR>\n" );
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document.write( "So we have found that x = -5/2<BR>\n" );
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document.write( "Step 5)<BR>\n" );
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document.write( "Check by substituting -5/2 for x in the original given equation:<BR>\n" );
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document.write( "9x + 7 = 5x - 3<BR>\n" );
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document.write( "9*(-5/2) + 7 = 5*(-5/2) - 3<BR>\n" );
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document.write( "Multiply out to get:<BR>\n" );
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document.write( "-45/2 + 7 = -25/2 -3<BR>\n" );
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document.write( "Multiply all terms of this equation (on both sides) by 2 to get rid of the denominators:<BR>\n" );
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document.write( "2*(-45/2) + 2*7 = 2*(-25/2) + 2*(-3)<BR>\n" );
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document.write( "-45 + 14 = -25 - 6<BR>\n" );
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document.write( "-31 = -31<BR>\n" );
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document.write( "Both sides of the equation are equal, so the answer is correct ... x = -5/2 which also<BR>\n" );
document.write( "can be written as x = -2.5 or x = -2 1/2.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and the procedures that you use to solve<BR>\n" );
document.write( "linear equations of this type.<BR>\n" );
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document.write( " </SPAN>\n" );
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