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**Chapter 4: Solving Inequalities**

4.5 Compound Inequalities

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**X > 5 and x < 7 written as 5 < x < 7**

Compound Inequality Two inequalities joined by the word “and” or the word “or” “And” compound inequalities are sometimes written all together: X > 5 and x < 7 written as 5 < x < 7

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Example 1 Write a compound inequality to represent the situation and graph the solution: All real numbers that are at least -2 and at most 4

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Example 1a Write a compound inequality to represent the situation and graph the solution: Today’s temperatures will be above 32⁰F but not as high as 40⁰F

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Example 1c Write a compound inequality to represent the situation and graph the solution: All real numbers greater than -2 but less than 9

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Example 1d Write a compound inequality to represent the situation and graph the solution: The books were priced between $3.50 and $6.00, inclusive

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Example 2 Solve -4 < r – 5 ≤ -1 and graph the solution

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Example 2a Solve -6 ≤ 3x < 15 and graph the solution

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Example 2b Solve -3 < 2x – 1 < 7 and graph the solution

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Example 2c Solve 7 < -3n + 1 ≤ 13 and graph the solution

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Example 3 The acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and 7.8, inclusive. The first two readings for a swimming pool are 7.4 and What possible values for the third reading p will make the average pH normal?

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Example 3a Suppose the first two readings for the acidity of water in a swimming pool are 7.0 and What possible values for the third reading will make the average pH normal?

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Example 4 Write a compound inequality that represents the situation and graph the solution: All real numbers that are less than -3 or greater than 7.

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Example 4a Write a compound inequality that represents the situation and graph the solution: Discounted fares are available to children 12 and under or to adults at least 60 years of age.

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Example 4b Write a compound inequality that represents the situation and graph the solution: All real numbers that are at most -5 or at least 3.

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Example 5 Solve 4v + 3 < -5 or -2v + 7 < 1 and graph the solution.

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Example 5a Solve -2x + 7 > 3 or 3x – 4 ≥ 5 and graph the solution

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Homework P. 230 6-38 even, 54

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