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Compound inequalities

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Intros
Lessons
  1. Introduction to compound inequalities

    i. Recap of inequalities symbols

    ii. Ideas of AND and OR

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Examples
Lessons
  1. Evaluate Compound Inequalities: OR

    Solve the following compound inequalities:

    4x−164x - 16 < 16  16\; OR   8x+15≤−1\;8x + 15 \leq -1

    1. Solve the following compound inequalities:

      4x+54x + 5 < 13  13\; OR   3x\;3x > 3939

      1. Evaluate Compound Inequalities: AND

        Solve the following compound inequalities:

        4x+304x + 30 > 34  34\; AND   12x−6\;12x - 6 > 1818

        1. Solve the following compound inequalities:

          −6x+2-6x + 2 > 20  20\; AND   13x+11≤50\;13x + 11 \leq 50

          1. Analyze the Alternate Form of Compound Inequalities: AND

            Solve the following compound inequalities:

            −5≤3x+1≤7-5 \leq 3x + 1 \leq 7

            1. Solve the following compound inequalities:

              −14-14 < 1−5x≤111 - 5x \leq 11

              1. Special Cases: No solution, All Real Numbers

                Solve the following compound inequalities:

                3x−33x - 3 < 9  9\; AND   6x+1\;6x + 1 > 3737

                1. Solve the following compound inequalities:

                  5x+65x + 6 < 36  36\; OR   −3x≤18\;-3x \leq 18

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                  Practice
                  Topic Notes
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                  If the relationship between the compound inequalities is OR and they point towards the same direction, you will pick the inequality which has a broader range.

                  If the relationship between the compound inequalities is AND and they point towards the same direction, you will pick the inequality which has a narrower range.

                  When you multiply or divide a negative number, the inequality symbol will be reversed.

                  Basic Concepts
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