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Math Help - Solve the inequity

  1. #1
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    Solve the inequity

    Solve the following inequity. Write the anwser in interval notation.

    1 + 2/x+1 greater or less than or equal to 2/x

    i got the intervals (-infinity, -2) U [-2, 1] U [1, infinity)

    Are these the correct intervals, and which ones are true?
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  2. #2
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    Quote Originally Posted by B-lap View Post
    Solve the following inequity. Write the anwser in interval notation.

    1 + 2/x+1 greater or less than or equal to 2/x

    i got the intervals (-infinity, -2) U [-2, 1] U [1, infinity)

    Are these the correct intervals, and which ones are true?
    the bold statement makes no sense ... fix it.
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  3. #3
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    less than or equal to
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  4. #4
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    Quote Originally Posted by B-lap View Post
    Solve the following inequity. Write the anwser in interval notation.

    1 + 2/x+1 less than or equal to 2/x

    i got the intervals (-infinity, -2) U [-2, 1] U [1, infinity)

    Are these the correct intervals ... no
    1 + \frac{2}{x+1} - \frac{2}{x} \le 0<br />

    \frac{x(x+1)}{x(x+1)} + \frac{2x}{x(x+1)} - \frac{2(x+1)}{x(x+1)} \le 0

    \frac{x^2 + x + 2x - 2x - 2}{x(x+1)} \le 0

    \frac{x^2 + x - 2}{x(x+1)} \le 0

    \frac{(x+2)(x-1)}{x(x+1)} \le 0

    critical values are x = -2, x = -1, x = 0 , and x = 1

    now check the inequality using x-values within each interval separated by the critical values of x.
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