document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100118>Question 100118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need you help with one problem. I just don't have a real example.<BR>\n" );
document.write( "2x-1  > 6x - 5<BR>\n" );
document.write( "      -     \r<BR>\n" );
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document.write( "Thank You, </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72918 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=72918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is very similar to a problem that was posted previously. You are given to solve:<BR>\n" );
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document.write( "2x-1 > 6x - 5<BR>\n" );
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document.write( "What this means you are asked to find the values for +x that will make 2x - 1 be greater<BR>\n" );
document.write( "than 6x - 5<BR>\n" );
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document.write( "You can work these as if the \">\" sign were an \"=\" with one exception. That means that the<BR>\n" );
document.write( "rules for solving equations apply ... except that if you MULTIPLY or DIVIDE both sides of<BR>\n" );
document.write( "the inequality by a negative quantity, you must also reverse the direction of the inequality<BR>\n" );
document.write( "sign.<BR>\n" );
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document.write( "Let's work this problem like an equation:<BR>\n" );
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document.write( "2x - 1 > 6x - 5<BR>\n" );
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document.write( "Get rid of the 6x on the right side by subtracting 6x from both sides:<BR>\n" );
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document.write( "2x - 6x - 1 > 6x - 6x - 5<BR>\n" );
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document.write( "Do the subtractions on both sides to get:<BR>\n" );
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document.write( "-4x - 1 > -5<BR>\n" );
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document.write( "Now as you would do with an equation, get rid of the -1 on the left side by adding +1<BR>\n" );
document.write( "to both sides:<BR>\n" );
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document.write( "-4x - 1 + 1 > -5 + 1<BR>\n" );
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document.write( "On the left side the - 1 + 1 cancel each other. On the right side the - 5 + 1 combine <BR>\n" );
document.write( "to result in -4. This makes the inequality:<BR>\n" );
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document.write( "-4x > -4<BR>\n" );
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document.write( "But the problem requires us to solve for +x. So, just as you would do in an equation<BR>\n" );
document.write( "let's solve for +x by dividing both sides by -4 because that is the multiplier of x.<BR>\n" );
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document.write( "-4x/-4 > -4/-4<BR>\n" );
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document.write( "The division results in:<BR>\n" );
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document.write( "x > 1<BR>\n" );
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document.write( "But don't forget the rule about the direction of the inequality sign. When you divide<BR>\n" );
document.write( "or multiply both sides by a minus quantity, you must also reverse the direction of the <BR>\n" );
document.write( "inequality sign.  We divided both sides by the minus quantity -4. Therefore, our answer must<BR>\n" );
document.write( "have the inequality going in the opposite direction from what it was just before we did the<BR>\n" );
document.write( "division by -4. Therefore, our answer is:<BR>\n" );
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document.write( "x < 1<BR>\n" );
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document.write( "This means that for any value of x that is less than +1, the value of 2x - 1 will be <BR>\n" );
document.write( "greater than the value of 6x - 5<BR>\n" );
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document.write( "Let's set x = to zero, just to do a \"confidence\" check. Since 0 is less than 1, the value<BR>\n" );
document.write( "we have chosen for x, we should find that 2x - 1 is greater than 6x - 5.  <BR>\n" );
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document.write( "When x is 0, then 2x - 1 equals -1 and 6x - 5 is 6(0) - 5 = 0 - 5 = -5. This makes the original<BR>\n" );
document.write( "inequality you were given as the problem become:<BR>\n" );
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document.write( "-1 > -5<BR>\n" );
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document.write( "That is true. -1 is greater than -5 because -1 lies to the right of -5 on a number line.<BR>\n" );
document.write( "Therefore, since this is true it helps to build your confidence that whenever x is less than<BR>\n" );
document.write( "1, the given inequality will be true.<BR>\n" );
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document.write( "Hope this also helps you to see how to do these problems.<BR>\n" );
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