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Solve Inequality

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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
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.

  • Solve Inequality -

    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.

  • Solve Inequality -

    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
    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:
    If for some reason the lower limit is excluded, it would be written as:
    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:

    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:

    (alternatively, ]-∞,-6]∪[0,8] )

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