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Compound Inequalities

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A compound inequality is an equation with two or more inequalities joined together with either “and” or “or”. For example: x ≤ -3 or x ≥ 2; x ≥ -7 and x ≤ 7

ii) 2(y-1) < 6 Or 2(y-1) > 10

These inequalities are connected with < or > symbol, so the solution will be the union of solutions of these two inequalities.

      Dividing both sides by 2,

       (y-1) < 3 or (y-1) > 5

        Adding 1 to both sides of the inequality, we get

        y<4  Or y>6

        Interval notation: 

Check Point

Solve the given compound inequalities and write the answer in interval notation:

Answer Key

       There is no overlap between the two inequalities, hence there is no solution to the compound inequality.

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