document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=344402>Question 344402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I desperately need help with a math problem. I've done it several different times, but every time I enter the answer I get, the program I do my homework on says it's wrong.\r<BR>\n" );
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document.write( "1 + |9t -6| = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246337 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=246337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equation is:<BR>\n" );
document.write( "1 + abs(9T-6) = 5\r<BR>\n" );
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document.write( "Subtract 1 from both sides of this equation to get:<BR>\n" );
document.write( "abs(9T-6) = 4\r<BR>\n" );
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document.write( "If abs(x) = y, this means that x = y if x is positive, and -x = y if x is negative.\r<BR>\n" );
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document.write( "In your equation, 9T-6 is equal to x, and 4 is equal to y.\r<BR>\n" );
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document.write( "You get:\r<BR>\n" );
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document.write( "9T-6 = 4 when (9T-6) is positive.\r<BR>\n" );
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document.write( "You get:\r<BR>\n" );
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document.write( "-(9T-6) = 4 when (9T-6) is negative.\r<BR>\n" );
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document.write( "Solve the equation for when T is positive.\r<BR>\n" );
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document.write( "You get 9T-6 = 4<BR>\n" );
document.write( "Add 6 to both sides of this equation to get 9T = 10<BR>\n" );
document.write( "Divide both sides of this equation by 9 to get T = (10/9).\r<BR>\n" );
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document.write( "Solve the equation for when T is negative.\r<BR>\n" );
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document.write( "You get -(9T-6) = 4<BR>\n" );
document.write( "Remove parentheses to get -9T + 6 = 4<BR>\n" );
document.write( "Subtract 6 from both sides of this equation to get -9T = -2<BR>\n" );
document.write( "Divide both sides of this equation by -9 to get T = (2/9).\r<BR>\n" );
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document.write( "Your answer is that T can be either (10/9) or (2/9).\r<BR>\n" );
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document.write( "Substitute in your original equation to see if this is true.\r<BR>\n" );
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document.write( "Your original equation is 1 + abs(9T-6) = 5<BR>\n" );
document.write( "Subtract 1 from both sides of this equation to get:<BR>\n" );
document.write( "abs(9T-6) = 4.\r<BR>\n" );
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document.write( "Substitute (10/9) for T to get:<BR>\n" );
document.write( "abs(9*(10/9)-6) = 4 which becomes:<BR>\n" );
document.write( "abs(10-6) = 4 which becomes:<BR>\n" );
document.write( "abs(4) = 4 which becomes:<BR>\n" );
document.write( "4 = 4 which is true, so the answer of T = (10/9) is good.\r<BR>\n" );
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document.write( "Substitute (2/9) for T to get:<BR>\n" );
document.write( "abs(9*(2/9)-6) = 4 which becomes:<BR>\n" );
document.write( "abs(2-6) = 4 which becomes:<BR>\n" );
document.write( "abs(-4) = 4 which becomes:<BR>\n" );
document.write( "4 = 4 which is true, so the anser of T = (2/9) is good.\r<BR>\n" );
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document.write( "Let me know if these are the correct answers.<BR>\n" );
document.write( "I believe that they are.\r<BR>\n" );
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document.write( "The main thing you do when solving absolute equation is to solve for when the expression is positive and to solve for when the expression is negative.\r<BR>\n" );
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document.write( "abs(expression) = answer becomes expression = answer when expression is positive.\r<BR>\n" );
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document.write( "abs(expression) = answer becomes - expression = answer when expression is negative.\r<BR>\n" );
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document.write( "The expression in your case was (9T-6).\r<BR>\n" );
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document.write( "If (x) is the expression, and y is the answer, then the equation becomes:\r<BR>\n" );
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document.write( "abs(x) = y if and only if:\r<BR>\n" );
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document.write( "x = y when x is positive.\r<BR>\n" );
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document.write( "-x = y when x is negative.\r<BR>\n" );
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document.write( "You will also see a rule that states:\r<BR>\n" );
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document.write( "abs(x) = y if and only if:\r<BR>\n" );
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document.write( "x = y when x is positive.\r<BR>\n" );
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document.write( "x = -y when x is negative.\r<BR>\n" );
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document.write( "This rule is derived from what I originally stated.\r<BR>\n" );
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document.write( "if -x = y, then multiply both sides of the equation by -1 to get x = -y.\r<BR>\n" );
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document.write( "That's what leads to the alternate form of the solution to the absolute value of equation.\r<BR>\n" );
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document.write( "It becomes more fun when you get to inequalities as you will see soon enough, if not already.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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