Question

Solve each compound inequality (show your work!)

Answer 1

Answer:  -1 < x < 8

                x = 3

                x ≠ 2

Step-by-step explanation:

Isolate x in the middle.  Perform operations to all 3 sides.

-6 < 2x - 4 < 12

+4        +4   +4

-2 < 2x       < 16

÷2    ÷2         ÷2

-1   <   x       <  8

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Isolate x.  Solve each inequality separately. Remember to flip the sign when dividing by a negative.

       4x ≤ 12       and       -7x ≤ 21

      ÷4    ÷4                 ÷-7     ÷-7

        x ≤ 3         and         x ≥  3

Since it is an "and" statement, x is the intersection of both inequalities.

When is x ≤ 3 and ≥ 3?    when x = 3

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Isolate x.  Solve each inequality separately.

    15x > 30       or           18x < -36

   ÷15   ÷15                   ÷18     ÷18

       x > 2          or              x <   2

Since it is an "or" statement, x is the union of both inequalities.

When we combine the inequalities, x is every value except 2.

x ≠ 2