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Math Help - How do you solve this inequality??

  1. #1
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    How do you solve this inequality??

    2x≥3x+6≥6x-6

    please explainn your answer, i dont know how to do it thanks
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  2. #2
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    Re: How do you solve this inequality??

    Quote Originally Posted by roger1505 View Post
    2x≥3x+6≥6x-6
    Check that posting; makes no sense...
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  3. #3
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    Re: How do you solve this inequality??

    It does make sense.....
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  4. #4
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    Re: How do you solve this inequality??

    Split into two inequalities: 2x \ge 3x+6 and 3x+6 \ge 6x-6 and solve each one.


    If 2x \ge 3x+6, solving for x we get x \le -6.


    For the second inequality, 3x+6 \ge 6x-6, subtract 3x from both sides to get 6 \ge 3x-6. Add 6 to both sides to get 12 \ge 3x \Rightarrow x \le 4.


    The solution set is the intersection of the sets defined by x \le -6 and x \le 4 (because x needs to satisfy both inequalities). This inequality follows the transitive property, so we do not need to worry about the inequality 2x \ge 6x-6. The solution set is x \le -6.
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