1. a 1.4 Sets, Inequalities, and Interval Notation
Determine whether a given number is a solution of an
inequality.
1.4
Sets, Inequalities, and Interval Notation
An inequality is a sentence containing
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

2. Determine whether the given number is a solution of the inequality.
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

3. Determine whether the given number is a solution of the inequality.
We substitute –3 for x and get or a true sentence. Therefore, –3 is a solution.
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

4. The graph of an inequality is a drawing that represents its solutions.
Graph on the number line.
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

5. Write interval notation for the solution set or the graph of an inequality.
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6. Write interval notation for the solution set or the graph of an inequality.
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7. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Write interval notation for the solution set or the graph of an inequality.
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
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8. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
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9. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
The Addition Principle for Inequalities c
Solve an inequality using the addition principle and the
multiplication principle and then graph the inequality.
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
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10. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
The Multiplication Principle for Inequalities
For any real numbers a and b, and any positive number c: c
Solve an inequality using the addition principle and the
multiplication principle and then graph the inequality.
For any real numbers a and b, and any negative number c:
Similar statements hold for
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
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11. c
Solve an inequality using the addition principle and the
multiplication principle and then graph the inequality.
The multiplication principle tells us that when we multiply or divide on both sides of an inequality by a negative number, we must reverse the inequality symbol to obtain an equivalent inequality.
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

12. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Translating “At Least” and “At Most” d
Solve applied problems by translating to inequalities.
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13. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Solve applied problems by translating to inequalities.
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14. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Solve applied problems by translating to inequalities.
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
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