Solving and Graphing Compound Inequalities Inequalities Containing and
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Solving and Graphing Compound Inequalities
Inequalities Containing and n To ride a roller coaster, you must be at least 52 inches tall, and your height cannot exceed 72 inches. n If h represents the height of the rider, we can write two inequalities to represent this. At least 52 inches Cannot exceed 72 inches h ≥ 52 and h ≤ 72 n n The inequalities h ≥ 52 and h ≤ 72 can be combined and written without using “and” as 52 ≤ h ≤ 72 Graph the inequality “sandwich” Variable is isolated
Inequalities Containing and You try! Solve, graph, and write in interval notation. 1. ) -2 < x – 3 < 4 2. ) -5 < 3 p + 7 ≤ 22
Inequalities Containing or n SNAKES Most snakes live where the temperature ranges from 750 F to 900 F. Write an inequality to represent temperatures where snakes will not thrive. Let t = temperature t < 75 or t > 90 n Graph the inequality “torpedo”
Inequalities Containing or You try! Solve, graph, and write in interval notation. 1. 5 n – 1 < -16 or -3 n – 1 < 8 2. The product of -5 and a number is greater than 35 or at least 10.
OPEN ENDED 1: Write a compound inequality containing and for which the graph is the empty set. Sample answer: x ≤ -4 and x ≥ 1 OPEN ENDED 2: Create an example of a compound inequality containing or that has infinitely many solutions. Sample answer: x ≤ 5 or x ≥ 1
Chemistry The acidity of the water in a swimming pool is considered normal if the average of three p. H readings is between 7. 2 and 7. 8. The first two readings for the swimming pool are 7. 4 and 7. 9. What possible values for the third reading p will make the average p. H normal?
The value for the third reading must be between 6. 3 and 8. 1, inclusive.
GEOMETRY The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side. x 9 4 a. ) Write and solve three inequalities to express the relationships among the measures of the sides of the triangle shown above. b. ) What are the possible lengths for the third side of the triangle? c. ) Write a compound inequality for the possible values of x.
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