document.write( "Question 902235: TABLE OF SIGNS
\n" ); document.write( "Suppose:
\n" ); document.write( "x + 10/(x − 17)^2 ≥ 0
\n" ); document.write( "Create a table of signs from this inequality.
\n" ); document.write( "Please explain how this is done. Because someone else poorly explained this process to me and now I feel way behind in my precalculus class.
\n" ); document.write( "Also:
\n" ); document.write( "Select the intervals below that can be combined to form the solution set for the given inequality.
\n" ); document.write( "NOTE: If the solution includes a interval such as ( -5 , 3 ], you should choose ONLY ( -5 , 3 ] and NOT ( -5 , 3 ). \r
\n" ); document.write( "\n" ); document.write( "(−∞, −10)
\n" ); document.write( "(−∞, −10]
\n" ); document.write( "[−10, 17)
\n" ); document.write( "[−10, 17]
\n" ); document.write( "(−10, 17)
\n" ); document.write( "(−10, 17 ]
\n" ); document.write( "(17, ∞)
\n" ); document.write( "[17, ∞)
\n" ); document.write( "(−10, ∞)
\n" ); document.write( "(−∞, 17)
\n" ); document.write( "[−10, ∞)
\n" ); document.write( "(−∞, 17] \r
\n" ); document.write( "\n" ); document.write( "Please explain how these are solved
\n" ); document.write( "THANK YOU \n" ); document.write( "
Algebra.Com's Answer #547206 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
First for any rational inequality, find the critical points where the numerator or the denominator equal zero.
\n" ); document.write( "In this case,
\n" ); document.write( "\"x%2B10=0\"
\n" ); document.write( "\"x=-10\"
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\n" ); document.write( "\"x-17=0\"
\n" ); document.write( "\"x=17\"
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\n" ); document.write( "So now break up the number line into three regions based on these critical numbers.
\n" ); document.write( "Values where the denominator equals zero are values that are not in the domain of the function since division by zero is undefined.
\n" ); document.write( "So for those values use ().
\n" ); document.write( "Region 1 : (\"infinity\",\"-10\"]
\n" ); document.write( "Region 2 : [\"-10\",\"17\")
\n" ); document.write( "Region 3 : (\"17\",\"infinity\")
\n" ); document.write( "For each region choose a point in the region (avoid the endpoints) and test the inequality.
\n" ); document.write( "If the inequality is satisfied, that region is part of the solution.
\n" ); document.write( "Otherwise, that region is not part of the solution.
\n" ); document.write( "Region 1 : Choose \"x=-11\"
\n" ); document.write( "\"%28-11%2B10%29%2F%28-11-17%29%5E2%3E=0\"
\n" ); document.write( "\"-1%2F%28-38%29%5E2%3E=0\"
\n" ); document.write( "False, Region 1 is not part of the solution region.
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\n" ); document.write( "Region 2 : Choose \"x=0\"
\n" ); document.write( "\"%2810%29%2F%2810-17%29%5E2%3E=0\"
\n" ); document.write( "\"%2810%29%2F%287%29%5E2%3E=0\"
\n" ); document.write( "True, Region 2 is part of the solution region.
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\n" ); document.write( "Region 3 : Choose \"x=18\"
\n" ); document.write( "\"%2818%2B10%29%2F%2818-17%29%5E2%3E=0\"
\n" ); document.write( "\"28%3E=0\"
\n" ); document.write( "True, Region 3 is part of the solution region.
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\n" ); document.write( "So the solution region is\r
\n" ); document.write( "\n" ); document.write( "[\"-10\",\"17\")U (\"17\",\"infinity\")
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\n" ); document.write( "In terms of table of signs,
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\n" ); document.write( "where LHS is Left Hand side of the equation, N is negative, P is positive. \n" ); document.write( "
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