document.write( "Question 67163This question is from textbook 0-534-49449-8
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document.write( "How would I solve the inequality 7<4x+3<21 and \r\n" );
document.write( "express the solution as an interval?
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Algebra.Com's Answer #47756 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "How would I solve the inequality 7<4x+3<21 and \r\n" );
document.write( "express the solution as an interval?\r\n" );
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document.write( " 7 < 4x + 3 < 21\r\n" );
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document.write( "The idea is to isolate x in the middle.\r\n" );
document.write( "Get rid of the 3 by adding -3 to all three sides:\r\n" );
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document.write( "  7 < 4x + 3 < 21\r\n" );
document.write( " -3       -3   -3\r\n" );
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document.write( "  4 < 4x     < 18\r\n" );
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document.write( "So we have\r\n" );
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document.write( "    4 < 4x < 18\r\n" );
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document.write( "Now we divide all three sides by the coefficient of x,\r\n" );
document.write( "which is 4.  Since we are dividing by a positive\r\n" );
document.write( "number we DO NOT reverse the inequalities as we do\r\n" );
document.write( "when we divide thru by a negative number:\r\n" );
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document.write( "    4     4x     18\r\n" );
document.write( "   ——— < ———— < ————\r\n" );
document.write( "    4      4      4\r\n" );
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document.write( "or\r\n" );
document.write( "                 9  \r\n" );
document.write( "        1 < x < ———\r\n" );
document.write( "                 2\r\n" );
document.write( "or\r\n" );
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document.write( "        1 < x < 4.5\r\n" );
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document.write( "On a number line this is graphed as\r\n" );
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document.write( " -2  -1   0   1   2   3   4   5   6   7          \r\n" );
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document.write( "It is an open circle at 1, because\r\n" );
document.write( "it is < and not <, and closed (dark\r\n" );
document.write( "circle) at 4.5, because it is < and not <.\r\n" );
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document.write( "The interval notation is a shorthand\r\n" );
document.write( "for this graph:\r\n" );
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document.write( "       (1, 4.5]\r\n" );
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document.write( "The \"(\" on the left represents the\r\n" );
document.write( "open circle, the 1 is the left endpoint\r\n" );
document.write( "of the shaded part, the 4.5 is the right endpoint\r\n" );
document.write( "of the shaded part, and the \"]\" represents\r\n" );
document.write( "the closed circle.\r\n" );
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document.write( "Edwin

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