document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118192>Question 118192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> when solving inequalities, how do you know whether to add or to subtract on both sides? Can you explain with an example? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86294 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=86294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can work inequalities just as you would work and equation ... same rules: \r<BR>\n" );
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document.write( "If you add a number on one side of the inequality you must also add the same number to the <BR>\n" );
document.write( "other side of the inequality. <BR>\n" );
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document.write( "If you subtract a number from one side of the inequality you must also subtract the same number <BR>\n" );
document.write( "from the other side of the inequality. <BR>\n" );
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document.write( "If you multiply one side of an inequality by a number, you must also multiply the other side<BR>\n" );
document.write( "of the inequality by the same number.<BR>\n" );
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document.write( "If you divide one side of an inequality by a number, you must also multiply the other side<BR>\n" );
document.write( "of the inequality by the same number.<BR>\n" );
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document.write( "One exception you must remember ... if you multiply or divide both sides of an inequality<BR>\n" );
document.write( "by a NEGATIVE quantity, then you must reverse the direction of the inequality sign each time <BR>\n" );
document.write( "you multiply or divide by a negative.<BR>\n" );
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document.write( "And, just as you do with an equation, you solve it for the positive value of the variable.<BR>\n" );
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document.write( "Suppose you have the inequality  2x + 5 < 5x - 1 and you want to solve it. You can sort <BR>\n" );
document.write( "of imagine that the inequality sign is an equal sign while you do the work.<BR>\n" );
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document.write( "First get rid of the + 5 on the left side by subtracting 5 from both sides. When you do that you<BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "2x < 5x - 6<BR>\n" );
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document.write( "Next get rid of the 5x on the right side by subtracting 5x from both sides, just as you would<BR>\n" );
document.write( "do in an equation. After that subtraction from both sides you have:<BR>\n" );
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document.write( "-3x < -6<BR>\n" );
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document.write( "You can now solve for +x by dividing both sides by -3 to get:<BR>\n" );
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document.write( "x < -6/-3 <BR>\n" );
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document.write( "BUT you divided both sides by -3 a negative number so you have to reverse the direction of<BR>\n" );
document.write( "the inequality sign which results in:<BR>\n" );
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document.write( "x > -6/-3<BR>\n" );
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document.write( "Now just do the division on the right side and you get the answer:<BR>\n" );
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document.write( "x > 2<BR>\n" );
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document.write( "Not too bad, once you get used to the process. You can check your answer by selecting a<BR>\n" );
document.write( "value of x that is greater than 2 and seeing if it works in the original inequality. The<BR>\n" );
document.write( "original inequality was:<BR>\n" );
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document.write( "2x + 5 < 5x - 1<BR>\n" );
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document.write( "Let x be 3 and it becomes:<BR>\n" );
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document.write( "2(3) + 5 < 5(3) - 1<BR>\n" );
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document.write( "Which simplifies to:<BR>\n" );
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document.write( "6 + 5 < 15 - 1<BR>\n" );
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document.write( "Combine the numbers on both sides and you have:<BR>\n" );
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document.write( "11 < 14<BR>\n" );
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document.write( "That's true ... 11 is less than 14. So that seems to work. Next let x = 2 which means that<BR>\n" );
document.write( "you have chosen a value for x that is NOT GREATER than 2. The original inequality is:<BR>\n" );
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document.write( "2x + 5 < 5x - 1<BR>\n" );
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document.write( "Substitute 2 for x and it becomes:<BR>\n" );
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document.write( "2(2) + 5 < 5(2) - 1<BR>\n" );
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document.write( "Do the multiplications and you get:<BR>\n" );
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document.write( "4 + 5 < 10 - 1<BR>\n" );
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document.write( "Combine the numbers on both sides and you have:<BR>\n" );
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document.write( "9 < 9<BR>\n" );
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document.write( "This is not true because 9 is not less than 9 ... it is equal to 9. It looks as if the answer<BR>\n" );
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document.write( "x > 2<BR>\n" );
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document.write( "is the correct solution to the problem.  <BR>\n" );
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document.write( "Hope this gives you some help in working inequality problems. If you still need additional help, <BR>\n" );
document.write( "re-post some more problems.<BR>\n" );
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document.write( "And Happy 2008 to you and yours ...<BR>\n" );
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