document.write( "Question 141191: p2+9p+14>0
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Algebra.Com's Answer #102835 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"p%5E2%2B9p%2B14%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28p%2B7%29%28p%2B2%29%3E0\"$ Factor the left side\r
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\n" ); document.write( "\n" ); document.write( " $\"%28p%2B7%29%28p%2B2%29=0\"$ 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( " $\"p%2B7=0\"$ or $\"p%2B2=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Solve for p in each case:\r
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\n" ); document.write( "\n" ); document.write( " $\"p=-7\"$ or $\"p=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our critical values are $\"p=-7\"$ and $\"p=-2\"$ \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( " $\"number_line%28+600%2C+-10%2C+10%2C-7%2C-2%29\"$ \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 $\"-7\"$ (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 $\"p=-8\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"p%5E2%2B9p%2B14%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-8%2B7%29%28-8%2B2%29%3E+0\"$ Plug in $\"p=-8\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"6%3E+0\"$ 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 (

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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is in between $\"-7\"$ and $\"-2\"$ :\r
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\n" ); document.write( "\n" ); document.write( "So let's pick $\"p=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"p%5E2%2B9p%2B14%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-4%2B7%29%28-4%2B2%29%3E+0\"$ Plug in $\"p=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"-6%3E+0\"$ 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 $\"-2\"$ (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 $\"p=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"p%5E2%2B9p%2B14%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-1%2B7%29%28-1%2B2%29%3E+0\"$ Plug in $\"p=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"6%3E+0\"$ 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 (

)

(

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