9.1 Math 9

Do the “Math Link” with a partner on page 339. Discuss in class. 1 Do the “Math Link” with a partner on page 339. Discuss in class. 1.a) Each gondola could hold a number of people that is less than or equal to 60 1.b) The first Ferris wheel could hold a number of people that is less than or equal to 2160 3.a) Amount of weight it can hold. Size of seats can only hold so many people. 3.b) Height of person. Age of person. Medical condition.

Linear inequalities are a way to compare quantities to analyze situations. An inequality is: a mathematical statement comparing expressions that may not be equal.  

Inequality Meaning a > b a < b a ≥ b a ≤ b a ≠ b Reading an inequality depends on the inequality symbol used: (p.342) Inequality Meaning a > b a < b a ≥ b a ≤ b a ≠ b

Inequality Meaning a > b a < b a ≥ b a ≤ b a ≠ b Reading an inequality depends on the inequality symbol used: (p.342) Inequality Meaning a > b  a is greater than b a < b  a is less than b a ≥ b  a is greater than or equal to b a ≤ b  a is less than or equal to b a ≠ b  a is not equal to b

Inequalities can be expressed three ways: Verbally “All numbers less than or equal to 0.25” Algebraically Using math symbols - Graphically Using diagrams or graphs like a

Inequalities Expressed as Number Lines: Represent x ≤ −5 on a number line Represent x > −5 on a number line Use a closed circle to represent this inequality Use an open circle to represent this inequality

The boundary point separates the values less than from the values greater than the specified value An open circle shows that the boundary point is not included in the solution. A closed circle shows that the boundary point is included in the solution.

Example 1 - In many provinces, you must be at least 16 years old to get a driver’s license. a) Sketch a number line to represent this situation. b) Represent this situation algebraically. Using a to represent age in years, a ≥ 16.

X > 4 Example 2 – Expressing Inequalities a) Express the inequality shown algebraically X > 4

Example 2 – Expressing Inequalities b) Represent n < -12 on a number line

2 ≥ X > -6 or 2 ≥ X and X > -6 x ≤ 2 and x > -6 Example 2 – Expressing Inequalities c) Write an inequality for the values shown on the number line 2 ≥ X > -6 or 2 ≥ X and X > -6 x ≤ 2 and x > -6

X ≤ -7 2x ≤ -14 Example 2 – Expressing Inequalities d) Show the possible values for x on a number line, if -7 ≥ x . *What is a different way to express −7 ≥ x algebraically? X ≤ -7 2x ≤ -14

Example 3 – Represent a Combination of Inequalities  Represent the temperature change from -19°C to 22°C both graphically and algebraically Using t to represent temperature then the change in temperature is written as t ≥ -19 and t ≤ 22. Or -19 ≤ t ≤ 22

By the way we are half way through the course. Summer School Summer Fun

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April 19, 2012 9.1 Assignment Corey “The Starter” Schneider 16, 17, 18, 21, 22 *23, *24, *25