Solve Inequality

posted by .

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.

  • 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] )

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math- Problem3

    Solve the following inequality and write your answer using interval notation. Please show all of your work. (1 / (x+8) ) ≤ ((8-5x)/43)
  2. Math - Problem4

    Solve the inequality. Express your solution using interval notation and please show all of your work. x^4 - 7x^2 - 14 > 0
  3. precalculus

    solve the inequality express your solution using interval notation x^4-7x^3+12x^2<0
  4. algebra

    Solve the following inequality and write your answer using interval notation . Please show all your work 10^3 + 6x^2 - 90x - 54 < 0
  5. algebra

    Solve the following inequality and write answer using interval notation. Please show all of your work. 2x-5/3x^4-x^3+275x-125>=0
  6. algebra

    Solve the inequality. Express your solution using notation and please show all of your work. x^4<16x^2
  7. Math

    Solve the inequality by first rewriting it as an equivalent inequality without absolute value bars. Express solution set using interval notation. | x+3 | +8 is less than or equal to 14 Thanks so much for helping me!
  8. calculus

    solve the following inequality. write your solution in interval notation. x^3+9x^2-108 less than or equal to 0 please show all work
  9. math

    solve the polynomial inequality and graph the solution set on a real number line. express the solution set in interval notation x^3+x^2+64x+64>0 show work please
  10. math-please help,need quickly

    solve the polynomial inequality and graph the solution set on a real num ber line. express the solution set in interval notation x^3+x^2+64x+64>0 please show work

More Similar Questions