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Solve the following inequalities. Write your answer using interval notation.\r
\n" ); document.write( "\n" ); document.write( "(x+4)(2x-3)>0
\n" ); document.write( "x+4=0 and 2x-3=0
\n" ); document.write( "x+4-4=0-4 and 2x-3+3=0+3
\n" ); document.write( "x=-4 and 2x=3
\n" ); document.write( "x=-4 and 2x/2=3/2
\n" ); document.write( "x=-4 and x=3/2
\n" ); document.write( "These are your critical numbers, they tell you the possible intervals, (-infinity,-4),(-4,3/2), (3/2,infinity):
\n" ); document.write( "Check the interval (-infinity,-4) by using a test number in that interval like -5
\n" ); document.write( "(-5+4)(2(-5)-3)>0 ?
\n" ); document.write( "(-1)(-13)>0
\n" ); document.write( "13>0 This is true.
\n" ); document.write( "This tells us that the interval (-infinity, -4) is in the solution.
\n" ); document.write( ":
\n" ); document.write( "Now test the interval (-4,3/2) with a test number like 0.
\n" ); document.write( "(0+4)(2*0-3)>0 ?
\n" ); document.write( "(4)(-3)>0
\n" ); document.write( "-12>0 This is not true so the interval (-4,3/2) is not part of the solution.
\n" ); document.write( ":
\n" ); document.write( "Now test the interval (3/2,infinity) with a test number like 2.
\n" ); document.write( "(2+4)(2*2-3)>0 ?
\n" ); document.write( "(6)(1)>0
\n" ); document.write( "6>0 This is true
\n" ); document.write( "This tells us that the interval (3/2,infinity) is part of the solution.
\n" ); document.write( "The Solution is: (-infinity,-4)U(3/2,infinity)
\n" ); document.write( ":\r
\n" ); document.write( "\n" ); document.write( "x^2-2x<8
\n" ); document.write( "x^2-2x-8<8-8
\n" ); document.write( "x^2-2x-8<0 Factor
\n" ); document.write( "(x-4)(x+2)<0
\n" ); document.write( "x-4=0 and x+2=0
\n" ); document.write( "x-4+4=0+4 and x+2-2=0-2
\n" ); document.write( "x=4 and x=-2
\n" ); document.write( "These tell you that your possible intervals are:(-infinity,-2),(-2,4), and (4,infinty)
\n" ); document.write( ":
\n" ); document.write( "Test the interval of (-infinity,-2) with a test number like, -3.
\n" ); document.write( "(-3-4)(-3+2)<0 ?
\n" ); document.write( "(-7)(-1)<0
\n" ); document.write( "7<0 This is not true.
\n" ); document.write( "(-infinty,-2) is not part of the solution.
\n" ); document.write( "Test the interval (-2,4) with a test number like 0.
\n" ); document.write( "(0-4)(0+2)<0 ?
\n" ); document.write( "-4(2)<0
\n" ); document.write( "-8<0 this is true.
\n" ); document.write( "(-2,4) is part of the solution.
\n" ); document.write( "Test the interval (4,infinity) with a test number like 5.
\n" ); document.write( "(5-4)(5+2)<0 ?
\n" ); document.write( "1(7)<0
\n" ); document.write( "7<0 this is not part of the soltuion.
\n" ); document.write( "The solution therefore is: (-2,4)
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "