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**Algebra 6-5 Solving Open Sentences Involving Absolute Value**

– 3 – 2 – | | | | | | | | | | – 5 – 4 – 3 – 2 – | | | | | | | | | | Harbour

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**Solving Open sentences involving absolute vale**

Section 6-5 Solving Open sentences involving absolute vale

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**Solving Open Sentences Involving Absolute Value**

Algebra 6-5 Solving Open Sentences Involving Absolute Value There are three types of open sentences that can involve absolute value. Consider the case | x | = n. | x | = 5 means the distance between 0 and x is 5 units If | x | = 5, then x = – 5 or x = 5. The solution set is {– 5, 5}. Solving Open Sentences Involving Absolute Value Harbour

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**Algebra 6-5 Solving Open Sentences Involving Absolute Value**

When solving equations that involve absolute value, there are two cases to consider: Case 1 The value inside the absolute value symbols is positive. Case 2 The value inside the absolute value symbols is negative. Equations involving absolute value can be solved by graphing them on a number line or by writing them as a compound sentence and solving it. Harbour

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**Solve an Absolute Value Equation**

Method 1 Graphing means that the distance between b and –6 is 5 units. To find b on the number line, start at –6 and move 5 units in either direction. The distance from –6 to –11 is 5 units. The distance from –6 to –1 is 5 units. Answer: The solution set is

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**Solve an Absolute Value Equation**

Method 2 Compound Sentence Write as or Case 1 Case 2 Original inequality Subtract 6 from each side. Simplify. Answer: The solution set is Example 5-1a

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**Solve an Absolute Value Equation**

Answer: {12, –2}

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**Write an Absolute Value Equation**

Write an equation involving the absolute value for the graph. Find the point that is the same distance from –4 as the distance from 6. The midpoint between –4 and 6 is 1. The distance from 1 to –4 is 5 units. The distance from 1 to 6 is 5 units. So, an equation is .

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**Write an Absolute Value Equation**

Answer: Check Substitute –4 and 6 into

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**Write an Absolute Value Equation**

Write an equation involving the absolute value for the graph. Answer:

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**Algebra 6-5 Solving Open Sentences Involving Absolute Value**

Consider the case | x | < n. | x | < 5 means the distance between 0 and x is LESS than 5 units If | x | < 5, then x > – 5 and x < 5. The solution set is {x| – 5 < x < 5}. Harbour

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**Algebra 6-5 Solving Open Sentences Involving Absolute Value**

When solving equations of the form | x | < n, find the intersection of these two cases. Case 1 The value inside the absolute value symbols is less than the positive value of n. Case 2 The value inside the absolute value symbols is greater than negative value of n. Harbour

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**Solve an Absolute Value Inequality (<)**

Then graph the solution set. Write as and Case 1 Case 2 Original inequality Add 3 to each side. Simplify. Answer: The solution set is

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**Solve an Absolute Value Inequality (<)**

Then graph the solution set. Answer:

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**Algebra 6-5 Solving Open Sentences Involving Absolute Value**

Consider the case | x | > n. | x | > 5 means the distance between 0 and x is GREATER than 5 units If | x | > 5, then x < – 5 or x > 5. The solution set is {x| x < – 5 or x > 5}. Harbour

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**Algebra 6-5 Solving Open Sentences Involving Absolute Value**

When solving equations of the form | x | > n, find the union of these two cases. Case 1 The value inside the absolute value symbols is greater than the positive value of n. Case 2 The value inside the absolute value symbols is less than negative value of n. Harbour

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**Solve an Absolute Value Inequality (>)**

Then graph the solution set. Write as or Case 1 Case 2 Original inequality Add 3 to each side. Simplify. Divide each side by 3. Simplify.

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**Solve an Absolute Value Inequality (>)**

Answer: The solution set is

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**Solve an Absolute Value Inequality (>)**

Then graph the solution set. Answer:

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**Algebra 6-5 Solving Open Sentences Involving Absolute Value**

In general, there are three rules to remember when solving equations and inequalities involving absolute value: If then or (solution set of two numbers) If then and (intersection of inequalities) If then or (union of inequalities) Harbour

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**Assignment Study Guide 6-5 (In-Class)**

Pages #’s 14-19, 24-35, 40, 41. (Homework)

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