document.write( "Question 50268: Graph the solution of each compound inequality on a number line.\r
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Algebra.Com's Answer #33406 by AnlytcPhil(1806) $\"\"$ $\"About$
You can put this solution on YOUR website!
Graph the solution of each compound inequality\r\n" );
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document.write( "The solution given before this is incomplete\r\n" );
document.write( "because you are supposed to combine them on\r\n" );
document.write( "ONE number line:\r\n" );
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document.write( "y - 2 < 4 AND y + 4 > 7\r\n" );
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document.write( "Solve the first one:  | Solve the second one:\r\n" );
document.write( "                      | \r\n" );
document.write( "y - 2 < 4             | y + 4 > 7    \r\n" );
document.write( "    y < 6             |     y > 3\r\n" );
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document.write( "So the simplified version is:\r\n" );
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document.write( "    y < 6 AND y > 3\r\n" );
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document.write( "################################################\r\n" );
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document.write( "Draw three number lines, like this:\r\n" );
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document.write( "--------------------------------\r\n" );
document.write( "-2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
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document.write( "--------------------------------\r\n" );
document.write( "-2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
document.write( "\r\n" );
document.write( "--------------------------------\r\n" );
document.write( "-2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
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document.write( "################################################\r\n" );
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document.write( "Mark the numbers 3 and 6 on all three\r\n" );
document.write( "number lines:\r\n" );
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document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
document.write( "\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
document.write( "\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "################################################\r\n" );
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document.write( "Label the first number line \" y < 6 \"\r\n" );
document.write( "Label the second number line \" y > 3 \"\r\n" );
document.write( "Label the third number line  \" y < 6 AND y > 3 \"\r\n" );
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document.write( " y < 6\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
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document.write( " y > 3\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
document.write( "\r\n" );
document.write( " y < 6 AND y > 3\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
document.write( "\r\n" );
document.write( "################################################\r\n" );
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document.write( "Since the first one is y < 6, shade the part\r\n" );
document.write( "left of 6\r\n" );
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document.write( " y < 6\r\n" );
document.write( "<=========================o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
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document.write( " y > 3\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
document.write( "\r\n" );
document.write( " y < 6 AND y > 3\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
document.write( "\r\n" );
document.write( "################################################\r\n" );
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document.write( "Since the second one is y > 3, shade the part\r\n" );
document.write( "right of 3:\r\n" );
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document.write( " y < 6\r\n" );
document.write( "<=========================o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
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document.write( " y > 3\r\n" );
document.write( " ----------------o===============>\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
document.write( "\r\n" );
document.write( " y < 6 AND y > 3\r\n" );
document.write( " ----------------o--------o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
document.write( "\r\n" );
document.write( "################################################\r\n" );
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document.write( "Now to shade the last number line, \r\n" );
document.write( "we will shade only the part where \r\n" );
document.write( "both the first number line is shaded \r\n" );
document.write( "AND the second one is shaded. Only \r\n" );
document.write( "the part between 3 and 6 is shaded in\r\n" );
document.write( "both the first number line AND the \r\n" );
document.write( "second. So we just shade that part on \r\n" );
document.write( "the third number line:\r\n" );
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document.write( " y < 6\r\n" );
document.write( "<=========================o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
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document.write( " y > 3\r\n" );
document.write( " ----------------o===============>\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8 \r\n" );
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document.write( " y < 6 AND y > 3\r\n" );
document.write( " ----------------o========o------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "That last number line is the final \r\n" );
document.write( "answer.  Sometimes teachers and \r\n" );
document.write( "books tell you to put parentheses \r\n" );
document.write( "if the end point is included and \r\n" );
document.write( "brackets if it's not included.  \r\n" );
document.write( "Neither of these endpoints\r\n" );
document.write( "is included, so the final answer in\r\n" );
document.write( "that case would be like this:\r\n" );
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document.write( " y < 6 AND y > 3\r\n" );
document.write( " ----------------(========)------\r\n" );
document.write( " -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "Incidentally y > 3 can be rewritten\r\n" );
document.write( "as 3 < y and so\r\n" );
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document.write( " 3 < y AND y < 6\r\n" );
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document.write( "can be written all together as\r\n" );
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document.write( "  3 < y < 6  \r\n" );
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document.write( "Edwin
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