document.write( "Question 190395This question is from textbook
\n" ); document.write( ": If I had this equation -5 £ 2x+1 < 11 and my final answer was -3 £ x < 5 and the interval notation is
\n" ); document.write( " [-3,5), what would the number line look like?\r
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Algebra.Com's Answer #142892 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I know you only wanted to see the number line, but I think\r\n" );
document.write( "I'll check to see if you have the right solution and interval\r\n" );
document.write( "notation. \r\n" );
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document.write( "-5 £ 2x+1 < 11\r\n" );
document.write( "-1      -1   -1   (subtracting from all three sides)\r\n" );
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document.write( "-6 £ 2x   < 10   \r\n" );
document.write( "-3 £  x   <  5   (dividing all\r\n" );
document.write( "                  three sides by a\r\n" );
document.write( "                  positive number,\r\n" );
document.write( "                  which means we \r\n" );
document.write( "                  leave the \r\n" );
document.write( "                  inequalities as \r\n" );
document.write( "                  they are.)\r\n" );
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document.write( "OK, so you solved it correctly!:\r\n" );
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document.write( "Let's draw a number line and number it, like this:\r\n" );
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document.write( "-5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8\r\n" );
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document.write( "Let's put a closed circle at -3 on the number line, because it\r\n" );
document.write( "involves \"or equal to\". I'll use the \"at\" symbol \" @ \" for a \r\n" );
document.write( "closed circle. \r\n" );
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document.write( "---------@--------------------------------------------\r\n" );
document.write( "-5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8 \r\n" );
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document.write( "Now let's put an open circle on the 5.  I'll use \r\n" );
document.write( "an open circle since it is strictly less and doesn't \r\n" );
document.write( "involve \"or equal to\". I'll use an \" o \" for an open \r\n" );
document.write( "circle.\r\n" );
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document.write( "---------@-------------------------------o------------\r\n" );
document.write( "-5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8 \r\n" );
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document.write( "Now we want to do some shading.  Here's the best way to think\r\n" );
document.write( "of this a different way:\r\n" );
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document.write( "-3 £ x  <  5\r\n" );
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document.write( "If x is in the middle, it's easier to see if you first break it \r\n" );
document.write( "up as \r\n" );
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document.write( "-3 £ x AND x < 5\r\n" );
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document.write( "And then write the £ as an equivalent ³ by reversing\r\n" );
document.write( "the first using the rule if A £ B  then B ³ A.\r\n" );
document.write( "So we have:\r\n" );
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document.write( "x ³ -3 AND x < 5\r\n" );
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document.write( "\"Greater than\" means \"to the right of\" on the number line and\r\n" );
document.write( "\"less than\" means \"to the left of\" on the number line.\r\n" );
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document.write( "So we shade the part of the number line that is both to the right of\r\n" );
document.write( "-3 and also to the left of 5, like this: \r\n" );
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document.write( "---------@===============================o------------\r\n" );
document.write( "-5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8\r\n" );
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document.write( "So that's the number line graph, now I'll explain the interval \r\n" );
document.write( "notation. It is just an abbreviation for the number line graph\r\n" );
document.write( "above. It is, as you correctly say, [-3,5)\r\n" );
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document.write( "You use a bracket, either \"[\" or this \"]\" depending on which side \r\n" );
document.write( "of the shading it's on, for a closed circle, \" @ \".\r\n" );
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document.write( "You use a parenthesis, either \"(\" or this \")\", depending on which \r\n" );
document.write( "side it's on, for an open circle, \" o \". The two numbers separated\r\n" );
document.write( "by a comma in between are the endpoints of the shaded region.\r\n" );
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document.write( "Edwin

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