Solve the inequality. Express your solution using interval notation and please show all of your work. X(x+6)(8-x) greater or equal to 0
x(x + 6)(8 – x) 0

College Agebra not calculus. thanks

Expert Answers

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`x(x+6)(8-x) >= 0`

`1)==> x >= 0 and x + 6 >= 0 and 8-x >= 0`

`==> x>=0 and x>= -6 and x <= 8`

`==> x in [0,oo) nn [-6,oo) nn (-oo, 8]`

`==> x in [0,8]`

`2) => x <= 0 and x+6 <= 0 and (8-x) >= 0`

`==> x in (-oo,0] nn (-oo, -6] nn (-oo, 8]`

`==> x in (-oo,-6]`

`3) x <= 0 and x+6 >= 0 and (8-x) <= 0`

`==> x in (-oo,0] nn [-6,oo) nn [8,oo)`

`==> x in phi`

`4) x >= 0 and (x+6) <= 0 and (8-x) <= 0`

`==> x in [0. oo) nn (-oo, -6] nn [8, oo)`

`==> x in phi`

Then, from (1) and (2) we conclude that the solution is :

`==> x in (-oo,-6] U [0,8]`

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