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Math Help - Inequalities?

  1. #1
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    Inequalities?

    Solve the following inequalities and express your solution in both set notation and interval notation:
    (a) | 2x - 1 | < 5

    (b) | 2x - 1 | > 5


    Need workings. Answer should be in set & interval notation
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  2. #2
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    Quote Originally Posted by federer View Post
    Solve the following inequalities and express your solution in both set notation and interval notation:
    (a) | 2x - 1 | < 5

    (b) | 2x - 1 | > 5


    Need workings. Answer should be in set & interval notation
    |2x - 1| = 2x - 1\, for 2x -1 \geq 0 \Rightarrow x \geq \frac{1}{2}.
    |2x - 1| = -(2x - 1)\, for 2x -1 < 0 \Rightarrow x < \frac{1}{2}.

    (a) Solve 2x - 1 < 5 => x < 3 AND x \geq \frac{1}{2}: \frac{1}{2} \leq x < 3.

    Solve -(2x - 1) < 5 => x > -2 AND x < \frac{1}{2}: -2  <  x < \frac{1}{2}.

    So the answer is \frac{1}{2} \leq x < 3 combined with -2  <  x < \frac{1}{2}. You can "express [this] solution in both set notation and interval notation".

    Do (b) in a similar way.
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