B5 Solving Linear Inequalities

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

Solve Graph 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 5-1a

A circle means that this point is not included in the solution set. 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 5-1b

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

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

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

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

Solve Graph 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 5-3a

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

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

Explore Let the number of gallons of gasoline that Alida buys. 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? Explore Let the number of gallons of gasoline that Alida buys. Plan The 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 $10.50. Write an inequality. Example 5-4a

$10.50. The cost of chips & soda plus the cost of gasoline is less than or equal to $10.50. 1.55 + 1.35g  10.50 Solve Original inequality Subtract 1.55 from each side. Simplify. Divide each side by 1.35. Simplify. Example 5-4b

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

Rental Costs Jeb wants to rent a car for his vacation 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 Example 5-4d