document.write( "Question 888525: I need help solving. Thank you\r
\n" ); document.write( "\n" ); document.write( "x^2 - 8x <= -15
\n" ); document.write( "

Algebra.Com's Answer #537462 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"x%5E2+-+8x+%3C=+-15\"\r\n" );
document.write( "\r\n" );
document.write( "Get 0 on the right, everything else on the left:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2+-+8x+%2B15+%3C=+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%28x-5%29%3C=0\"\r\n" );
document.write( "\r\n" );
document.write( "The critical numbers are the numbers which either make\r\n" );
document.write( "the left side 0 or undefined.\r\n" );
document.write( "\r\n" );
document.write( "The critical numbers are 3 and 5.\r\n" );
document.write( "\r\n" );
document.write( "Place these numbers on a number line:\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  9\r\n" );
document.write( "\r\n" );
document.write( "we test any value less than 3, say 0, in the inequality\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%28x-5%29%3C=0\"\r\n" );
document.write( "\"%280-3%29%280-5%29%3C=0\"\r\n" );
document.write( "\"%28-3%29%28-5%29%3C=0\"\r\n" );
document.write( "\"15%3C=0\"\r\n" );
document.write( "\r\n" );
document.write( "That's false so we do not shade the number line to the\r\n" );
document.write( "left of 3\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  9\r\n" );
document.write( "\r\n" );
document.write( "we test any value between 3 and 5, say 4, in the inequality\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%28x-5%29%3C=0\"\r\n" );
document.write( "\"%284-3%29%284-5%29%3C=0\"\r\n" );
document.write( "\"%281%29%28-1%29%3C=0\"\r\n" );
document.write( "\"-1%3C=0\"\r\n" );
document.write( "\r\n" );
document.write( "That's true so we shade the number line between 3 and 5.\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  9\r\n" );
document.write( "\r\n" );
document.write( "we test any value to the right of 5, say 6, in the inequality\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%28x-5%29%3C=0\"\r\n" );
document.write( "\"%286-3%29%286-5%29%3C=0\"\r\n" );
document.write( "\"%283%29%281%29%3C=0\"\r\n" );
document.write( "\"3%3C=0\"\r\n" );
document.write( "\r\n" );
document.write( "That's false so we do not shade the number line to the right of 5.\r\n" );
document.write( "\r\n" );
document.write( "Next we test the critical points themselves:\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  9\r\n" );
document.write( "\r\n" );
document.write( "Test 3\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%28x-5%29%3C=0\"\r\n" );
document.write( "\"%283-3%29%283-5%29%3C=0\"\r\n" );
document.write( "\"%280%29%28-2%29%3C=0\"\r\n" );
document.write( "\"0%3C=0\"\r\n" );
document.write( "\r\n" );
document.write( "That's true so we darken the circle at 3:\r\n" );
document.write( "\r\n" );
document.write( "----------------●=====o------------  \r\n" );
document.write( "-2 -1  0  1  2  3  4  5  6  7  8  9\r\n" );
document.write( "\r\n" );
document.write( "Test 3\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%28x-5%29%3C=0\"\r\n" );
document.write( "\"%285-3%29%285-5%29%3C=0\"\r\n" );
document.write( "\"%282%29%280%29%3C=0\"\r\n" );
document.write( "\"0%3C=0\"\r\n" );
document.write( "\r\n" );
document.write( "----------------●=====●------------  \r\n" );
document.write( "-2 -1  0  1  2  3  4  5  6  7  8  9\r\n" );
document.write( "\r\n" );
document.write( "That's true so we darken the circle at 5 also.\r\n" );
document.write( "\r\n" );
document.write( "The interval notation for the solution is [3,5]\r\n" );
document.write( "\r\n" );
document.write( "The set builder notation is  \"matrix%281%2C5%2C++++%22%7B%22%2Cx%2C%22%7C%22%2C3%3C=x%3C=5%2C%22%7D%22+%29\" \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );