document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73856>Question 73856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not sure if this is the right page for this. Can someone help me solve this problem. I'm trying to make head and tails out of it.\r<BR>\n" );
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document.write( "5 < 2(a+1)-3(1-a)\r<BR>\n" );
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document.write( "What i'm getting is 5 < -1a-1 not sure if right solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52824 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=52824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "5 < 2(a+1)-3(1-a)<BR>\n" );
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document.write( "You can operate on this just as you would an equation, with a major exception that I'll discuss <BR>\n" );
document.write( "later. The goal is to solve for \"a\" in the inequality just as you would solve for \"a\" if<BR>\n" );
document.write( "this were and equation ... having an = sign in place of the < sign.<BR>\n" );
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document.write( "Begin by doing the two distributed multiplications on the right side to get:<BR>\n" );
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document.write( "5 < 2a + 2 - 3 + 3a<BR>\n" );
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document.write( "Combine like terms on the right side. The 2a and the 3a add to 5a and the +2 and -3 add to -1.<BR>\n" );
document.write( "Substitute these values into the inequality and you get:<BR>\n" );
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document.write( "5 < 5a -1<BR>\n" );
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document.write( "Now we need to get rid of the -1 on the right side.  Do this by adding +1 to both sides of <BR>\n" );
document.write( "the inequality:<BR>\n" );
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document.write( "5 +1 < 5a -1 +1<BR>\n" );
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document.write( "On the left side add the 5 and +1 to get 6 and on the right side the -1 and +1 cancel each<BR>\n" );
document.write( "other out.  Therefore, the inequality now becomes:<BR>\n" );
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document.write( "6 < 5a<BR>\n" );
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document.write( "Finally, solve for \"a\" by dividing both sides by 5. This gives you:<BR>\n" );
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document.write( "6/5 < a<BR>\n" );
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document.write( "Read this as \"a\" must be bigger than 6/5.  You can also write the answer as:<BR>\n" );
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document.write( "a > 6/5<BR>\n" );
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document.write( "The \"arrow\" points to the smaller term.<BR>\n" );
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document.write( "Let's check by letting a = 1. That is less than 6/5 so the original inequality should not<BR>\n" );
document.write( "work for the value a = 1. Try it:<BR>\n" );
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document.write( "5 < 2(a+1)-3(1-a) and when a = 1 this becomes<BR>\n" );
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document.write( "5 < 2(1+1) - 3(1-1)<BR>\n" );
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document.write( "5 < 2(2) - 3(0)<BR>\n" );
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document.write( "5 < 4 ... just as you should expect.  This does not work because a was less than 6/5 not<BR>\n" );
document.write( "greater than.<BR>\n" );
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document.write( "Let's do a similar check by letting x = 2.  That is greater than 6/5 so it shoul make the <BR>\n" );
document.write( "inequality work.<BR>\n" );
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document.write( "5 < 2(a+1)-3(1-a) and let a = 2<BR>\n" );
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document.write( "5 < 2(2+1) - 3(1 - 2)<BR>\n" );
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document.write( "5 < 2(3) - 3(-1)<BR>\n" );
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document.write( "5 < 6 + 1<BR>\n" );
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document.write( "5 < 7 <BR>\n" );
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document.write( "5 is less than 7, so this time our check worked, as it was supposed to do because we<BR>\n" );
document.write( "used a value of a greater than 6/5.  Our answer is good.<BR>\n" );
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document.write( "Previously I mentioned that you could work inequalities just as you would an equation.  There<BR>\n" );
document.write( "is an exception, however.  That exception is that whenever you multiply or divide both<BR>\n" );
document.write( "sides of an inequality by a negative number, you must reverse the direction of the inequality.<BR>\n" );
document.write( "We did not have to make use of this rule in this particular problem.<BR>\n" );
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document.write( "Hope this helps you to understand inequalities a little better.<BR>\n" );
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document.write( " </SPAN>\n" );
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