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Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

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Exercise 33 Page 211

Try to rewrite this inequality as a compound inequality.

Solution Set: -5 < x < 5
Graph:

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We are asked to find and graph the solution set for all possible values of x in the given inequality. |x|<5 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number less than 5 away from the midpoint in the positive direction and any number less than 5 away from the midpoint in the negative direction.

Absolute Value Inequality:& |x| < 5 Compound Inequality:& -5 < x < 5 This compound inequality means that the distance between x and 0 is greater than -5 and less than 5. x>-5 and x<5 The solution to this type of compound inequality is the overlap of the solution sets. Let's recombine our cases back into one compound inequality. First Solution Set:& x < 5 Second Solution Set:& -5 < x Intersecting Solution Set:& -5 < x < 5

Graph

The graph of this inequality includes all values from -5 to 5, not inclusive. We show this by using open circles on the endpoints.

Subchapter links

Lesson Check p.210

Practice and Problem-Solving Exercises p.211-213

Standardized Test Prep p.213

Mixed Review p.213

Exercise 33 Page 211

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