Solve Inequality

Solve the inequality. Express your solution using interval notation and please show all of your work.
x(x + 6)(8 – x) >= 0


I need help, I guess I'm not understanding the interval notation portion.

I know, that when

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

that the statement is true.

but when I got my paper back it said that I got it wrong. I'm guessing that because it is not solve using interval notation, but I'm clueless.

  1. 0
asked by Armando
  1. the solution would be

    x ≤ -6 OR 0 ≤ x ≤ 8

    It might have been marked wrong since you used AND

    You should have been taught whichever "interval notation" your course is using.

    posted by Reiny
  2. There are different ways to represent an interval. The following is a summary.

    The most common one is
    x ≤ -6 OR 0 ≤ x ≤ 8
    as Reiny has put it.

    Others use a specialized notation as follows:
    The lower and then upper limits are written in order from left to right, separated by a comma, such as
    0,8
    The inclusion or exclusion of each limit is indicated by a square bracket or parenthesis accordingly.
    In the above example, since 0 and 8 are included in the interval, the interval would be written as:
    [0,8]
    If for some reason the lower limit is excluded, it would be written as:
    (0,8].
    A variation of the notation would write the square bracket pointing outwards to mean exclusion, such as:
    ]0,8] to say the same thing as (0,8].

    For the other limit, which goes from -∞ (excluded) to -6 (included), would be written as:
    (-∞-6].

    To join the two using logical operators, we would use the ∪ for "or", and ∩ for "and".

    Thus the final answer for the above problem would be written as:
    (-∞,-6]∪[0,8]

    (alternatively, ]-∞,-6]∪[0,8] )

    posted by MathMate

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