document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108052>Question 1108052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the correct solution set that satisfies the inequality\r<BR>\n" );
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document.write( "5x+2&#8805;7(x+2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723058 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=723058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x + 2 >= 7 * (x + 2)\r<BR>\n" );
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document.write( "simplify to get 5x + 2 >= 7x + 14\r<BR>\n" );
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document.write( "subtract 5x from both sides of the equation and subtract 14 from both sides of the equation to get 2 - 14 >= 7x - 5x.\r<BR>\n" );
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document.write( "combine like terms to get -12 >= 2x\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get -6 >= x\r<BR>\n" );
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document.write( "this is the same as x <= -6.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "you could also have solved it this way:\r<BR>\n" );
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document.write( "start with 5x + 2 >= 7x + 14\r<BR>\n" );
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document.write( "subtract 7x from both sides of the equation and subtract 2 from both sides of the equation to get 5x - 7x >= 14 - 2\r<BR>\n" );
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document.write( "combine like terms to get -2x >= 12\r<BR>\n" );
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document.write( "divide both sides of the equation by -2 to get x <= -6.\r<BR>\n" );
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document.write( "note that multiplying or dividing both sides of an inequality reverses the inequality.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "5 > 3<BR>\n" );
document.write( "multiply both sides by -1 gets you -5 < -3\r<BR>\n" );
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document.write( "since division is just another form of multiplication, it works for division as well.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "10 < 20<BR>\n" );
document.write( "divide both sides by -2 gets you -5 > -10\r<BR>\n" );
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document.write( "division by -2 is the same as multiplication by -1/2\r<BR>\n" );
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document.write( "10 < 20<BR>\n" );
document.write( "multiply both sides by -1/2 gets you -5 > -10.\r<BR>\n" );
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document.write( "anyway, back to the problem at hand.\r<BR>\n" );
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document.write( "your solution is the x <= -6.\r<BR>\n" );
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document.write( "to confirm replace x in the original equation with -8, -6, -4.\r<BR>\n" );
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document.write( "original equation is 5x + 2 >= 7 * (x + 2)\r<BR>\n" );
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document.write( "when x = -8, this becomes -38 >= -42 which is true.<BR>\n" );
document.write( "when x = -6, this becomes -28 >= -28 which is true.<BR>\n" );
document.write( "when x = -4, this becomes -18 >= -14 which is false.\r<BR>\n" );
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document.write( "solution is confirmed to be good because, when x <=-6, the original equation is true, and when x > -6, the original equation is false.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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