document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95838>Question 95838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help with this one? I don't understand.\r<BR>\n" );
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document.write( "Solve the Inequality<BR>\n" );
document.write( "2(x-4)+7<5-x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69819 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=69819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can work problems of this sort using the same procedures that you use for solving an<BR>\n" );
document.write( "equation. There is one exception ... if you multiply or divide both sides by a negative<BR>\n" );
document.write( "quantity, then you must reverse the direction of the inequality sign.<BR>\n" );
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document.write( "Let's do the problem. You were given:<BR>\n" );
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document.write( "2(x - 4) + 7 < 5 - x<BR>\n" );
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document.write( "Do the distributed multiplication on the left side by multiplying 2 times each of the two<BR>\n" );
document.write( "terms inside the parentheses.  When you multiply 2 times the terms in parentheses the inequality<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "2x - 8 + 7 < 5 - x<BR>\n" );
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document.write( "On the left side you can combine the -8 and the +7 and get -1. This simplifies the inequality<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "2x - 1 < 5 - x<BR>\n" );
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document.write( "Now you can get rid of the -x on the right side by adding x to both sides. On the left<BR>\n" );
document.write( "side when you add x it combines with the 2x to give you 3x. On the right side when you<BR>\n" );
document.write( "add x it combines with the -x and they cancel each other out. The inequality then is:<BR>\n" );
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document.write( "3x - 1 < 5<BR>\n" );
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document.write( "Now get rid of the -1 on the left side by adding +1 to both sides. On the left side the<BR>\n" );
document.write( "+1 combines with the -1 and they cancel each other. On the right side the +1 combines with<BR>\n" );
document.write( "the +5 and the result is +6. This makes the inequality:<BR>\n" );
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document.write( "3x < 6<BR>\n" );
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document.write( "Now solve for +x by dividing both sides by +3 because +3 is the multiplier of x. When you<BR>\n" );
document.write( "do this division to both sides the inequality becomes:<BR>\n" );
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document.write( "x < 6/3 <BR>\n" );
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document.write( "which simplifies to;<BR>\n" );
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document.write( "x < 2.<BR>\n" );
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document.write( "This means that the original inequality will be true if x is less than +2, and it will not <BR>\n" );
document.write( "be true if x is greater than +2. Let's try it. Suppose we let x be +1. That is less than<BR>\n" );
document.write( "+2 so the original inequality should be true.  The original inequality is:<BR>\n" );
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document.write( "2(x - 4) + 7 < 5 - x<BR>\n" );
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document.write( "If we substitute 1 for x it becomes:<BR>\n" );
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document.write( "2(1 - 4) + 7 < 5 - (+1)<BR>\n" );
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document.write( "On the left side the numbers in the parentheses combine to -3 and that gets multiplied<BR>\n" );
document.write( "by 2. So the inequality becomes<BR>\n" );
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document.write( "-6 + 7 < 5 - 1<BR>\n" );
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document.write( "Now the numbers on the left side (-6 + 7) combine to +1 and the numbers on the right (5 and -1) <BR>\n" );
document.write( "combine to +4. So when x is +1 the inequality becomes:<BR>\n" );
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document.write( "+1 < +4<BR>\n" );
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document.write( "That certainly is true because +1 is less than +4.<BR>\n" );
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document.write( "Now what if we let x = +3. That is greater than x = +2 so the inequality should not work. <BR>\n" );
document.write( "Start with the original inequality:<BR>\n" );
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document.write( "2(x - 4) + 7 < 5 - x<BR>\n" );
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document.write( "and substitute +3 for x to make the inequality become:<BR>\n" );
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document.write( "2(3 - 4) + 7 < 5 - (+3)<BR>\n" );
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document.write( "In the parentheses the +3 and the -4 combine to give -1 and that gets multiplied by the<BR>\n" );
document.write( "2 to become -2. So the inequality becomes:<BR>\n" );
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document.write( "-2 + 7 < 5 - 3<BR>\n" );
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document.write( "On the left side the -2 and the +7 combine to give +5. On the right side the 5 and the<BR>\n" );
document.write( "-3 combine to give +2. So when x = +3 the inequality becomes:<BR>\n" );
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document.write( "+5 < +2<BR>\n" );
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document.write( "That's not true! +5 is not less than +2. So when x is +3 the inequality does not work.<BR>\n" );
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document.write( "When we started this check we said that if x was less than +2 the inequality would work<BR>\n" );
document.write( "and if x was not less than +2 the inequality would not work. We let x be +1 which is<BR>\n" );
document.write( "less than +2 and found that the inequality did work. Then we let x be +3 which is greater<BR>\n" );
document.write( "than +2 and we found the inequality did not work.  It looks as if our solution of:<BR>\n" );
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document.write( "x < 2<BR>\n" );
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document.write( "is a good solution.<BR>\n" );
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document.write( "Hope that this helps you to understand the problem and how we went about finding a limit<BR>\n" );
document.write( "on the values that x could be to make the inequality work.<BR>\n" );
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document.write( "Note that we work this using the same procedures that you would use to solve an equation.<BR>\n" );
document.write( "Since we did not multiply or divide both sides by a minus number we did not need to reverse <BR>\n" );
document.write( "the direction of the inequality sign.<BR>\n" );
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document.write( " </SPAN>\n" );
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