document.write( "Question 189712: x^2-x-20>0 \n" ); document.write( "

Algebra.Com's Answer #142352 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-x-20%3E0\"$ Start with the given inequality\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B4%29%28x-5%29%3E0\"$ Factor the left side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B4%29%28x-5%29=0\"$ Set the left side equal to zero\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Set each individual factor equal to zero:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2B4=0\"$ or $\"x-5=0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solve for x in each case:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=-4\"$ or $\"x=5\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our critical values are $\"x=-4\"$ and $\"x=5\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now set up a number line and plot the critical values on the number line\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"number_line%28+600%2C+-10%2C+10%2C-4%2C5%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's pick some test points that are near the critical values and evaluate them.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is less than $\"-4\"$ (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 $\"x=-5\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-x-20%3E0\"$ Start with the given inequality\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28-5%29%5E2-%28-5%29-20%3E+0\"$ Plug in $\"x=-5\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"10%3E+0\"$ Evaluate and simplify the left side\r
\n" ); document.write( "
\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( "
\n" ); document.write( "\n" ); document.write( "So part our solution in interval notation is (

)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is in between $\"-4\"$ and $\"5\"$ :\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's pick $\"x=0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-x-20%3E0\"$ Start with the given inequality\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"0%5E2-0-20%3E+0\"$ Plug in $\"x=0\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-20%3E+0\"$ Evaluate and simplify the left side\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is greater than $\"5\"$ (notice how it's to the right of the rightmost endpoint):\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's pick $\"x=6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-x-20%3E0\"$ Start with the given inequality\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"6%5E2-6-20%3E+0\"$ Plug in $\"x=6\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"10%3E+0\"$ Evaluate and simplify the left side\r
\n" ); document.write( "
\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( "
\n" ); document.write( "\n" ); document.write( "So part our solution in interval notation is (

)

(

)\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );