pre-calculus

please help me with thisone thanks

solve the inequality algebraically. Express the solution in interval notation. (x-8)^2/x^2-36 > 0

  1. 👍 0
  2. 👎 0
  3. 👁 279
  1. Consider the equation:
    (x-8)^2/(x^-36) = 0
    (x-8)^2/((x+6)(x-6)) = 0

    "critical values are -6,6,8

    There are 4 segments on the number line of x which we should look at
    1. x < -6
    2. x between -6 and 6
    3. x between 6 and 8
    4. x > 8

    I usually take an arbitrary value in each segment, and test it in the original. We don't actually have to work out the value, just consider the signs.
    In this case, since the top is squared, we only have to look at the denominator's sign.

    1. let x = -10 ----+/+ > 0 , good
    2. let x = 0, --- +/- < 0 , no good
    3. let x = 7, --- +/+> 0 , good
    4. let x = 10 --- +/+ > 0 good

    so x < -6 OR x > 6, x is a real number.

    (The above is a rather general solution. In this case we could have just looked at the denominator.
    clearly we cannot have it become negative. It was easy to see that would happen between -6 and 6 for values of x)

    1. 👍 0
    2. 👎 0
  2. i don't get it so whick would be the solution or answer

    1. 👍 0
    2. 👎 0
  3. "so x < -6 OR x > 6, x is a real number"
    is the answer.
    As Reiny explained, there are two segments to the answer, hence the "OR".

    In interval notation, it would be:
    (-∞,-6)∪(6,∞).
    The (round) parentheses mean that the boundary values are excluded from the interval.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Solve the inequality. Expression solution set using interval notation and graph the solution set using a number line. -15x+3

  2. algebra

    solve the inequality. Express the solution using interval notation and graph the solution set on the real number line x-4/x^2-4 greater or equal to O

  3. algebra

    Solve the following rational inequality. Write the solution in interval notation. Show the number line and breaking points or graph of the polynomial with the part of the graph that is the solution (x-4)(x+2)/(x-3)(x+5) ¡Ü0

  4. calculus

    use a sign chart to solve inequality. Express answers in interval notation. x^2+6

  1. Algebra

    Solve the inequality: x+8 over x-1 > OR = 0 Write the solution set in interval notation. Show work/explanation.

  2. Algebra 2

    Write the solution to the given inequality in interval notation. [-3,-1) (-3,-1] (-∞,-3) U [-1,∞) (-∞,-3] U (-1,∞)

  3. math

    solve the compound inequality write the solution in interval notation 2u+4>-6 and 3u-6> -3

  4. College algebra

    use interval notation to express the solution set of the inequality |2x + 3|> or equal to 9

  1. Algebra

    solve each inequality algebraically and give the answer by using interval notation. 5-9y

  2. calculus

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

  3. pre cal

    solve the inequality express your solution in interval notation (x - 4)^2/ (x -6) (x + 6) > 0 Help me!

  4. Algebra

    solve the following inequality. write the solution in interval notation and graph it. [2y + 4] < 10 ( the [ ] are in place of absolute values , i don't have them on my keyboard) Thanks so much!

You can view more similar questions or ask a new question.