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Contents Lesson 1-1Expressions and Formulas Lesson 1-2Properties of Real Numbers Lesson 1-3Solving Equations Lesson 1-4Solving Absolute Value Equations Lesson 1-5Solving Inequalities Lesson 1-6Solving Compound and Absolute Value Inequalities

Lesson 6 Contents Example 1Solve an “and” Compound Inequality Example 2Solve an “or” Compound Inequality Example 3Solve an Absolute Value Inequality (<) Example 4Solve an Absolute Value Inequality (>) Example 5Solve a Multi-Step Absolute Value Inequality Example 6Write an Absolute Value Inequality

Example 6-1a Solve Graph the solution set on a number line. Method 1Write the compound inequality using the word and. Then solve each inequality. and Method 2Solve both parts at the same time by adding 2 to each part. Then divide each part by 3.

Example 6-1b Graph the solution set for each inequality and find their intersection. y  4y  4

Example 6-1c Solve Graph the solution set on a number line. Answer:

Example 6-2a Solve each inequality separately. or Answer: The solution set is Solveor Graph the solution set on a number line.

Example 6-2b Answer: Solve Graph the solution set on a number line.

You can interpretto mean that the distance between d and 0 on a number line is less than 3 units. To maketrue, you must substitute numbers for d that are fewer than 3 units from 0. Example 6-3a All of the numbers between –3 and 3 are less than 3 units from 0. SolveGraph the solution set on a number line. Answer: The solution set is Notice that the graph of is the same as the graph of d > –3 and d < 3.

Example 6-3b Answer: SolveGraph the solution set on a number line.

Example 6-4a You can interpretto mean that the distance between d and 0 on a number line is greater than 3 units. To maketrue, you must substitute values for d that are greater than 3 units from 0. All of the numbers not between –3 and 3 are greater than 3 units from 0. Answer: The solution set is Notice that the graph of is the same as the graph of SolveGraph the solution set on a number line.

Example 6-4b SolveGraph the solution set on a number line. Answer:

Example 6-5a Solve Graph the solution set on a number line. Solve each inequality. or is equivalent to Answer: The solution set is.

Example 6-5b Solve Graph the solution set on a number line. Answer:

Example 6-6a Housing According to a recent survey, the average monthly rent for a one-bedroom apartment in one city is $750. However, the actual rent for any given one- bedroom apartment might vary as much as $250 from the average. Write an absolute value inequality to describe this situation. Let the actual monthly rent. The rent for an apartment can differ from the average by as much as$250. Answer:  250

Answer: The solution set is The actual rent falls between $500 and $1000, inclusive. Solve the inequality to find the range of monthly rent. Example 6-6b Rewrite the absolute value inequality as a compound inequality. Then solve for r. –r–r r –r–r

Health The average birth weight of a newborn baby is 7 pounds. However, this weight can vary by as much as 4.5 pounds. a. Write an absolute value inequality to describe this situation. b. Solve the inequality to find the range of birth weights for newborn babies. Example 6-6c Answer: Answer:The birth weight of a newborn baby will fall between 2.5 pounds and 11.5 pounds, inclusive.

End of Lesson 6