document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083260>Question 1083260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all real numbers t such that 2/3t - 1 < t + 7 &#8804; -2t + 15. Give your answer as an interval. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697285 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=697285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> break these up into 2 separate inequalities.\r<BR>\n" );
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document.write( "start with 2/3 * t - 1 < t + 7 <= -2t + 15\r<BR>\n" );
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document.write( "the first set of inequalities is:\r<BR>\n" );
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document.write( "2/3 * t - 1 < t + 7<BR>\n" );
document.write( "add 1 to both sides to get:<BR>\n" );
document.write( "2/3 * t < t + 8<BR>\n" );
document.write( "subtract t from both sides to get:<BR>\n" );
document.write( "2/3 * t - t < 8<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "-1/3 * t < 8<BR>\n" );
document.write( "multiply both sides by 3 to get:<BR>\n" );
document.write( "-t < 24<BR>\n" );
document.write( "multiply both sides by -1 to get:<BR>\n" );
document.write( "t > -24<BR>\n" );
document.write( "multiplying both sides by -1 reverses the inequality.<BR>\n" );
document.write( "solution for the first set of inequalities is t > -24\r<BR>\n" );
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document.write( "the second set of inequalities is:\r<BR>\n" );
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document.write( "t + 7 <= -2 * t + 15<BR>\n" );
document.write( "subtract 7 from both sides to get:<BR>\n" );
document.write( "t <= -2 * t + 8<BR>\n" );
document.write( "add 2t to both sides to get:<BR>\n" );
document.write( "3 * t <= 8<BR>\n" );
document.write( "divide both sides by 3 to get:<BR>\n" );
document.write( "t <= 8/3<BR>\n" );
document.write( "solution for the second set of inequalities is t <= 8/3\r<BR>\n" );
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document.write( "your solution is that t > -24 and t <= 8/3\r<BR>\n" );
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document.write( "this can be written as -24 < t <= 8/3\r<BR>\n" );
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document.write( "in interval notation, this would be written as:\r<BR>\n" );
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document.write( "(-24,8/3]\r<BR>\n" );
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document.write( "you can test this out with various values of t to ensure the inequality is correct.\r<BR>\n" );
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document.write( "the inequality statement to test is:\r<BR>\n" );
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document.write( "2/3 * t - 1 < t + 7 <= -2t + 15\r<BR>\n" );
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document.write( "in order for the statement to be true, all parts of the inequality must be true.\r<BR>\n" );
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document.write( "2/3 * t - 1 must be smaller than t + 7 AND t + 7 must be smaller than or equal to -2t + 15\r<BR>\n" );
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document.write( "i checked and it all looks good, so i'm reasonably certain that the solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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