document.write( "Question 147153: (x+18)(x-2)(x+11)>0
\n" ); document.write( "I need to use at least one inequality or compound inequality to express the answer in the form of a solution set. I cannot figure out how to do this!
\n" ); document.write( "I thank you so much for any help! \n" ); document.write( "

Algebra.Com's Answer #107477 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28x%2B11%29%28x-2%29%28x%2B18%29%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B11%29%28x-2%29%28x%2B18%29=0\"$ 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( " $\"x%2B11=0\"$ , $\"x-2=0\"$ or $\"x%2B18=0\"$ \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( " $\"x=-11\"$ , $\"x=2\"$ or $\"x=-18\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our critical values are $\"x=-11\"$ , $\"x=2\"$ and $\"x=-18\"$ \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( " $\"number_line%28+600%2C+-20%2C+20%2C-11%2C2%2C-18%29\"$ \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 $\"-18\"$ (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 $\"x=-19\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B27x%5E2%2B140x-396%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-19%2B11%29%28-19-2%29%28-19%2B18%29%3E+0\"$ Plug in $\"x=-19\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"-168%3E+0\"$ 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 in between $\"-18\"$ and $\"-11\"$ :\r
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\n" ); document.write( "\n" ); document.write( "So let's pick $\"x=-14\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B27x%5E2%2B140x-396%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-14%2B11%29%28-14-2%29%28-14%2B18%29%3E+0\"$ Plug in $\"x=-14\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"192%3E+0\"$ 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 $\"-11\"$ and $\"2\"$ :\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( " $\"x%5E3%2B27x%5E2%2B140x-396%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-4%2B11%29%28-4-2%29%28-4%2B18%29%3E+0\"$ Plug in $\"x=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"-588%3E+0\"$ 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 $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B27x%5E2%2B140x-396%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%283%2B11%29%283-2%29%283%2B18%29%3E+0\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"294%3E+0\"$ 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( "Here's a graph to prove it\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-30%2C+10%2C+-630%2C+300%2C+%28x%2B11%29%28x-2%29%28x%2B18%29%29+\"$ Graph of $\"y=%28x%2B11%29%28x-2%29%28x%2B18%29\"$
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