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Solve the inequality | x^2-5x | < 6Show complete solution and explain the answer.

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spock6 | Student, Undergraduate | (Level 1) Honors

Posted October 17, 2011 at 10:34 PM via web

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Solve the inequality | x^2-5x | < 6

Show complete solution and explain the answer.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted October 17, 2011 at 10:51 PM (Answer #1)

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`I x^2 -5x I < 6`

`==> (x^2-5x) < 6`

`==> x^2 -5x -6 < 0`

`==> (x-6)(x+1) < 0`

`==> x-6 < 0 and x+1 > 0 ==> x < 6and x >-1 => x = (-1,6)`

`==> x-6>0 and x+1 <0 ==> x >6 and x <-1 ==> x= phi`

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`==> -(x^2-5) < 6`

`==> -x^2 +5 <6`

`==> -x^2 +5x -6 <0`

`==> x^2 -5x +6 >0`

`==> (x-2)(x-3) >0`

`==> x-2>0 and x-3>0 ==> x>2 andx>3 ==> x = (3,oo)`

`==> x-2<0 and x-3<0 ==> x<2 and x<3 ==> x = (-oo, 2)`

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`==> x in (-oo,2)U(-1,6)U(3,oo)= R-{ -1, 2, 3, 6}`

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