# Solve Inequality

posted by .

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.

• 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
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] )

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