document.write( "Question 87233: Please Help. I am no good with graphing
\n" ); document.write( "Solve and graph the solution set:
\n" ); document.write( "a)5y + 3 < -2 or y - 7 > 0
\n" ); document.write( "b) x - 9 < 3x - 4 < x + 8
\n" ); document.write( "PLEASE HELP!!!!!!!!! \n" ); document.write( "
Algebra.Com's Answer #63185 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Please Help. I am no good with graphing\r\n" );
document.write( "Solve and graph the solution set:\r\n" );
document.write( "a)5y + 3 < -2 or y - 7 > 0\r\n" );
document.write( "b) x - 9 < 3x - 4 < x + 8\r\n" );
document.write( "PLEASE HELP!!!!!!!!!\r\n" );
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document.write( "a)5y + 3 < -2 or y - 7 > 0\r\n" );
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document.write( "Solve each part:\r\n" );
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document.write( "5y + 3 < -2 or y - 7 >  0\r\n" );
document.write( "    -3   -3       +7   +7 \r\n" );
document.write( "-------------------------\r\n" );
document.write( "5y     < -5 or y     >  7\r\n" );
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document.write( "    5y < -5 or y > 7\r\n" );
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document.write( "     y < -1 or y > 7\r\n" );
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document.write( "Draw three number lines with a closed circle \r\n" );
document.write( "at the boundary points (closed because it's \r\n" );
document.write( "\"<\" and not \"<\"):\r\n" );
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document.write( "y < -1                  \r\n" );
document.write( "-----------l-------------l----------\r\n" );
document.write( "          -1              7      \r\n" );
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document.write( "y > 7                     \r\n" );
document.write( "-----------l-------------l----------\r\n" );
document.write( "          -1              7  \r\n" );
document.write( "                                                                            \r\n" );
document.write( "y < -1 or y > 7  \r\n" );
document.write( "-----------l-------------l----------\r\n" );
document.write( "          -1              7\r\n" );
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document.write( "Shade the first one to the left of -1, because\r\n" );
document.write( "\"less than\" is \"left\":\r\n" );
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document.write( "y < -1\r\n" );
document.write( "<===========l------------l----------\r\n" );
document.write( "           -1             7      \r\n" );
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document.write( "Shade the second one to the right of 7, because\r\n" );
document.write( "\"greater than\" is \"right\":\r\n" );
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document.write( "y > 7\r\n" );
document.write( "-----------l-------------l==========>\r\n" );
document.write( "          -1             7  \r\n" );
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document.write( "Now since the word between the inequalities is \"OR\" \r\n" );
document.write( "and not \"AND\", we shade all parts of the final\r\n" );
document.write( "number line if it is shaded on the first one OR if \r\n" );
document.write( "it is shaded on the second one.\r\n" );
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document.write( "So the final number line is:\r\n" );
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document.write( "y < -1 or y > 7  \r\n" );
document.write( "<============l-------------l==========>\r\n" );
document.write( "            -1             7    \r\n" );
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document.write( "Now we imagine that there is a \"negative infinity\"\r\n" );
document.write( "on the far left and an \"infinity\" on the far right.\r\n" );
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document.write( "So the interval notation is\r\n" );
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document.write( "(-oo, -1] U [7, oo)\r\n" );
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document.write( "b) x - 9 < 3x - 4 < x + 8\r\n" );
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document.write( "Add -x + 9 to all three sides:\r\n" );
document.write( "\r\n" );
document.write( " x - 9 < 3x - 4 <  x + 8\r\n" );
document.write( "-x + 9   -x + 9 < -x + 9\r\n" );
document.write( "------------------------\r\n" );
document.write( "     0 < 2x + 5 <     17\r\n" );
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document.write( "Add -5 to all three sides:\r\n" );
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document.write( "     0 < 2x + 5 < 17\r\n" );
document.write( "    -5       -5   -5\r\n" );
document.write( "------------------------\r\n" );
document.write( "    -5 < 2x     < 12\r\n" );
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document.write( "Divide all three sides by 2,\r\n" );
document.write( "to get only x in the middle:\r\n" );
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document.write( "    -2.5 < x < 6\r\n" );
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document.write( "That means \r\n" );
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document.write( "-2.5 < x  AND  x < 6\r\n" );
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document.write( "which is the same as\r\n" );
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document.write( " x > -2.5 AND x < 6\r\n" );
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document.write( "Draw three number lines with an open circle at \r\n" );
document.write( "the boundary points (open because it's \">\", \"<\" \r\n" );
document.write( "and not \"<\",\">:\r\n" );
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document.write( " x > -2.5                  \r\n" );
document.write( "-----------o-------------o----------\r\n" );
document.write( "         -2.5            6      \r\n" );
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document.write( " x < 6                     \r\n" );
document.write( "-----------o-------------o----------\r\n" );
document.write( "         -2.5            6  \r\n" );
document.write( "                                                                            \r\n" );
document.write( " x > -2.5 and x > 6  \r\n" );
document.write( "-----------o-------------o----------\r\n" );
document.write( "         -2.5            6\r\n" );
document.write( "\r\n" );
document.write( "Shade the first one to the right of -2.5, because\r\n" );
document.write( "\"greater than\" is \"right\":\r\n" );
document.write( "\r\n" );
document.write( " x > -2.5\r\n" );
document.write( "-----------o========================>\r\n" );
document.write( "         -2.5            6      \r\n" );
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document.write( "Shade the second one to the left of 6, because\r\n" );
document.write( "\"less than\" is \"left\":\r\n" );
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document.write( " x < 6\r\n" );
document.write( "<========================o----------\r\n" );
document.write( "         -2.5            6  \r\n" );
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document.write( "Now since the word between the inequalities this\r\n" );
document.write( "time is \"AND\" and not \"OR\", we shade only the parts \r\n" );
document.write( "of the final number line if it is shaded on the \r\n" );
document.write( "first one AND shaded on the second one.\r\n" );
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document.write( "So the final number line shaded is:\r\n" );
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document.write( " x > -2.5 and x > 6  \r\n" );
document.write( "-----------o=============o----------\r\n" );
document.write( "         -2.5            6\r\n" );
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document.write( "In interval notation that is \r\n" );
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document.write( "          (-2.5, 6)\r\n" );
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document.write( "Edwin
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