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Contents Lesson 1-5Solving Inequalities Lesson 1-6Solving Compound and Absolute Value Inequalities

Lesson 5 Contents Example 1Solve an Inequality Using Addition or Subtraction Example 2Solve an Inequality Using Multiplication or Division Example 3Solve a Multi-Step Inequality Example 4Write an Inequality

Example 5-1a SolveGraph the solution set on a number line. Original inequality Subtract 4y from each side. Simplify. Subtract 2 from each side. Simplify. Rewrite with y first.

Example 5-1b Answer: Any real number greater than –5 is a solution of this inequality. A circle means that this point is not included in the solution set.

Example 5-1c Answer: SolveGraph the solution set on a number line.

Example 5-2a SolveGraph the solution set on a number line. –40  p Simplify. p  –40 Rewrite with p first. Original inequality Divide each side by –0.3, reversing the inequality symbol.

Example 5-2b Answer: The solution set is A dot means that this point is included in the solution set.

Example 5-2c SolveGraph the solution set on a number line. Answer:

Example 5-3a SolveGraph the solution set on a number line. Original inequality Multiply each side by 2. Add –x to each side. Divide each side by –3, reversing the inequality symbol.

Example 5-3b Answer: The solution set isand is graphed below.

Example 5-3c SolveGraph the solution set on a number line. Answer:

Example 5-4a Consumer Costs Alida has at most $10.50 to spend at a convenience store. She buys a bag of potato chips and a can of soda for $1.55. If gasoline at this store costs $1.35 per gallon, how many gallons of gasoline can Alida buy for her car, to the nearest tenth of a gallon? ExploreLet the number of gallons of gasoline that Alida buys. PlanThe total cost of the gasoline is 1.35g. The cost of the chips and soda plus the total cost of the gasoline must be less than or equal to $ Write an inequality.

Example 5-4b The cost of chips & soda plus the cost of gasoline is less than or equal to $ g  Divide each side by Solve Original inequality Subtract 1.55 from each side. Simplify.

Example 5-4c Answer: Alida can buy up to 6.6 gallons of gasoline for her car. ExamineSince is actually greater than 6.6, Alida will have enough money if she gets no more than 6.6 gallons of gasoline.

Example 5-4d Rental Costs Jeb wants to rent a car for his vacation. Value Cars rents cars for $25 per day plus $0.25 per mile. How far can he drive for one day if he wants to spend no more that $200 on car rental? Answer: up to 700 miles

End of Lesson 5

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

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