document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88089>Question 88089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how can I Solve and graph the solution please help\r<BR>\n" );
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document.write( "7(x - 3) &#707;5x -14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64002 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=64002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "7(x-3) > 5x - 14<BR>\n" );
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document.write( "Except for a rule, you can work with inequalities just as you would work with equations.<BR>\n" );
document.write( "The exception is that if you multiply or divide both sides of an inequality by a negative <BR>\n" );
document.write( "quantity then you must reverse the direction of the inequality sign.  In this problem<BR>\n" );
document.write( "you do not need to use this rule. <BR>\n" );
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document.write( "Let's begin by doing the distributed multiplication on the left side of the inequality.<BR>\n" );
document.write( "This multiplication results in:<BR>\n" );
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document.write( "7x - 21 > 5x - 14<BR>\n" );
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document.write( "Just as you would do if this were an equation, you collect all the terms involving <BR>\n" );
document.write( "the variable x on one side and all the terms that are just numbers on the other side.<BR>\n" );
document.write( "Begin by getting rid of the 5x on the right side by subtracting 5x from both sides of<BR>\n" );
document.write( "the inequality. When you subtract 5x from both sides, the result is:<BR>\n" );
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document.write( "2x - 21 > -14<BR>\n" );
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document.write( "Next, get rid of the -21 on the left side. Do this by adding +21 to both sides. When you<BR>\n" );
document.write( "do this addition you get:<BR>\n" );
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document.write( "2x > +7<BR>\n" );
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document.write( "Finally, solve for x by dividing both sides by +2. When you do this division, the result<BR>\n" );
document.write( "is:<BR>\n" );
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document.write( "x > 7/2<BR>\n" );
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document.write( "You can graph this on the number line. On the number line put a dot at +7/2 which is<BR>\n" );
document.write( "to say put a dot at 3.5 or 3 1/2.  <BR>\n" );
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document.write( "Then on the number line x can be any number that is greater than +7/2, that is to say<BR>\n" );
document.write( "that x is any number that lies to the right of the point +7/2 on the number line. On<BR>\n" );
document.write( "this graph you can make the number line to the right of +7/2 a heavier, broader line to<BR>\n" );
document.write( "indicate that x can be any value on the heavier line. One of the ways that you can indicate<BR>\n" );
document.write( "that on the graph that +7/2 is not in the solution set is to use a \"(\" symbol immediately to <BR>\n" );
document.write( "the right of +7/2. This will show that as you move from right to left the heavier<BR>\n" );
document.write( "line ends just before the point +7/2.<BR>\n" );
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document.write( "Just to build our confidence that we have the correct answer, let' select a couple<BR>\n" );
document.write( "of values for x and try them in the original equation. Let's first let x be +3. According<BR>\n" );
document.write( "to our answer, that value of x is smaller than +7/2 so it should not work in the inequality.<BR>\n" );
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document.write( "The original inequality is:<BR>\n" );
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document.write( "7(x - 3) > 5x - 14<BR>\n" );
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document.write( "Substitute +3 for x and you get:<BR>\n" );
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document.write( "7(3 - 3) > 5(3) - 14<BR>\n" );
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document.write( "7(0) > 15 - 14<BR>\n" );
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document.write( "0 > 1<BR>\n" );
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document.write( "But zero is not greater than 1. So when x = +3 the inequality does not work, and we had<BR>\n" );
document.write( "said it should not.<BR>\n" );
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document.write( "Now let's try letting x = +4 which is slightly bigger than +7/2. Substitute +4 for x<BR>\n" );
document.write( "in the original inequality:<BR>\n" );
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document.write( "7(x - 3) > 5x - 14<BR>\n" );
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document.write( "7(4 - 3) > 5(4) - 14<BR>\n" );
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document.write( "7(1) > 20 - 14<BR>\n" );
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document.write( "7 > 6<BR>\n" );
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document.write( "This is true! 7 is greater than 6 and so when x is +4 the inequality does work.<BR>\n" );
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document.write( "This helps to confirm that +7/2 is the critical point on the number line where the value<BR>\n" );
document.write( "of x changes one from that will not satisfy the inequality to one that will.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to find the range of variables<BR>\n" );
document.write( "that will satisfy inequalities. </SPAN>\n" );
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