document.write( "Question 151578: \"+x%5E2%2B4x%2B3%3E0+\".\r
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Algebra.Com's Answer #111461 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'll do the first two to get you started\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B4x%2B3%3E0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B3%29%28x%2B1%29%3E0\" Factor the left side\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B3%29%28x%2B1%29=0\" Set the left side equal to zero\r
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\n" ); document.write( "\n" ); document.write( "Set each individual factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B3=0\" or \"x%2B1=0\" \r
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\n" ); document.write( "\n" ); document.write( "Solve for x in each case:\r
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\n" ); document.write( "\n" ); document.write( "\"x=-3\" or \"x=-1\" \r
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\n" ); document.write( "\n" ); document.write( "So our critical values are \"x=-3\" and \"x=-1\" \r
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\n" ); document.write( "\n" ); document.write( "Now set up a number line and plot the critical values on the number line\r
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\n" ); document.write( "\n" ); document.write( "\"number_line%28+600%2C+-10%2C+10%2C-3%2C-1%29\"\r
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\n" ); document.write( "\n" ); document.write( "So let's pick some test points that are near the critical values and evaluate them.\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is less than \"-3\" (notice how it's to the left of the leftmost endpoint):\r
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\n" ); document.write( "\n" ); document.write( "So let's pick \"x=-4\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B4x%2B3%3E0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%28-4%2B3%29%28-4%2B1%29%3E+0\" Plug in \"x=-4\"\r
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\n" ); document.write( "\n" ); document.write( "\"3%3E+0\" Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.\r
\n" ); document.write( "\n" ); document.write( " So part our solution in interval notation is ()\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is in between \"-3\" and \"-1\":\r
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\n" ); document.write( "\n" ); document.write( "So let's pick \"x=-2\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B4x%2B3%3E0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%28-2%2B3%29%28-2%2B1%29%3E+0\" Plug in \"x=-2\"\r
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\n" ); document.write( "\n" ); document.write( "\"-1%3E+0\" Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is greater than \"-1\" (notice how it's to the right of the rightmost endpoint):\r
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\n" ); document.write( "\n" ); document.write( "So let's pick \"x=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B4x%2B3%3E0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%280%2B3%29%280%2B1%29%3E+0\" Plug in \"x=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"3%3E+0\" Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.\r
\n" ); document.write( "\n" ); document.write( " So part our solution in interval notation is ()\r
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\n" ); document.write( "\n" ); document.write( "So the solution in interval notation is:\r
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\n" ); document.write( "\n" ); document.write( "() ()\r
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\n" ); document.write( "\n" ); document.write( "Here's a graph to visually verify the answer\r
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\n" ); document.write( "\n" ); document.write( "\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%2B3%29%28x%2B1%29%29+\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-2x-3%3C0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B1%29%28x-3%29%3C0\" Factor the left side\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B1%29%28x-3%29=0\" Set the left side equal to zero\r
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\n" ); document.write( "\n" ); document.write( "Set each individual factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B1=0\" or \"x-3=0\" \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solve for x in each case:\r
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\n" ); document.write( "\n" ); document.write( "\"x=-1\" or \"x=3\" \r
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\n" ); document.write( "\n" ); document.write( "So our critical values are \"x=-1\" and \"x=3\" \r
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\n" ); document.write( "\n" ); document.write( "Now set up a number line and plot the critical values on the number line\r
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\n" ); document.write( "\n" ); document.write( "\"number_line%28+600%2C+-10%2C+10%2C-1%2C3%29\"\r
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\n" ); document.write( "\n" ); document.write( "So let's pick some test points that are near the critical values and evaluate them.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is less than \"-1\" (notice how it's to the left of the leftmost endpoint):\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's pick \"x=-2\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-2x-3%3C0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%28-2%2B1%29%28-2-3%29%3C+0\" Plug in \"x=-2\"\r
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\n" ); document.write( "\n" ); document.write( "\"5%3C+0\" Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is in between \"-1\" and \"3\":\r
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\n" ); document.write( "\n" ); document.write( "So let's pick \"x=1\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-2x-3%3C0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%281%2B1%29%281-3%29%3C+0\" Plug in \"x=1\"\r
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\n" ); document.write( "\n" ); document.write( "\"-4%3C+0\" Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.\r
\n" ); document.write( "\n" ); document.write( " So part our solution in interval notation is ()\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is greater than \"3\" (notice how it's to the right of the rightmost endpoint):\r
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\n" ); document.write( "\n" ); document.write( "So let's pick \"x=4\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-2x-3%3C0\" Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( "\"%284%2B1%29%284-3%29%3C+0\" Plug in \"x=4\"\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5%3C+0\" Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.\r
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\n" ); document.write( "\n" ); document.write( "So the solution in interval notation is:\r
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\n" ); document.write( "\n" ); document.write( "()\r
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\n" ); document.write( "\n" ); document.write( "Here's a graph to visually verify the answer \r
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\n" ); document.write( "\n" ); document.write( "\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%2B1%29%28x-3%29%29+\"
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