Compound inequalities

Compound inequalities

Lessons

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.

  • Introduction
    Introduction to compound inequalities

    i. Recap of inequalities symbols

    ii. Ideas of AND and OR


  • 1.
    Evaluate Compound Inequalities: OR

    Solve the following compound inequalities:

    4x164x - 16 < 16  16\; OR   8x+151\;8x + 15 \leq -1


  • 2.
    Solve the following compound inequalities:

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


  • 3.
    Evaluate Compound Inequalities: AND

    Solve the following compound inequalities:

    4x+304x + 30 > 34  34\; AND   12x6\;12x - 6 > 1818


  • 4.
    Solve the following compound inequalities:

    6x+2-6x + 2 > 20  20\; AND   13x+1150\;13x + 11 \leq 50


  • 5.
    Analyze the Alternate Form of Compound Inequalities: AND

    Solve the following compound inequalities:

    53x+17-5 \leq 3x + 1 \leq 7


  • 6.
    Solve the following compound inequalities:

    14-14 < 15x111 - 5x \leq 11


  • 7.
    Special Cases: No solution, All Real Numbers

    Solve the following compound inequalities:

    3x33x - 3 < 9  9\; AND   6x+1\;6x + 1 > 3737


  • 8.
    Solve the following compound inequalities:

    5x+65x + 6 < 36  36\; OR   3x18\;-3x \leq 18