9 solving inequalities

9 Inequalities January 21, 2013

9 Inequalities

9 Inequalities January 21, 2013

10 2 3 4 5 6 7 8 9 10­1­2­3­4­5­6­7­8­9­10

1. Graph x = 9

2. Graph x ≥ 9

3. Graph x < 9

9 Inequalities January 21, 2013

Linear Inequalities in 2 Variables

"An inequality in the two variables x and y describes a region in the Cartesian plane. The ordered pair (x, y) is a solution to a linear inequality if the inequality is true when the values of x and y are substituted into the inequality. The set of points that satisfy a linear inequality can be called the solution set, or solution region."

9 Inequalities January 21, 2013

Steps for Graphing Inequalities

1. Draw the line2. Choose a reasonable test point3. Test the point and ask, "Does it satisfy the inequality?"4. Use the result from Part 3 to shade in the appropriate region

9 Inequalities January 21, 2013

Example: Graph 10x ­ 5y > 0

9 Inequalities January 21, 2013

Example: Determine if the point (­2, 4) is a part of the solution of the line 2x + 3y ≤ 6

9 Inequalities January 21, 2013

Example: Write an inequality to represent the following graph:

9 Inequalities January 21, 2013

9 Inequalities January 21, 2013

Quadratic Inequalities in One Variable

On a number line, find the numbers that satisfy the inequality.

STEPS1. Factor (if possible) to find the roots2. Use either the Sign Analysis Method to determine

positives and negatives to see which numbers fits the inequality.

9 Inequalities January 21, 2013

Example . Solve ­x2 + x + 12 < 0

9 Inequalities January 21, 2013

Your turn!Solve x2 ­ 2x ­ 3 ≤ 0

9 Inequalities January 21, 2013

Quadratic Inequalities in Two Variables

Exact same procedure as linear inequalities except now you have a quadratic instead of a line!

1. Draw the quadratic function.2. Choose a reasonable test point3. Test the point and ask, "Does it satisfy the inequality?"4. Use the result from Part 3 to shade in the appropriate region

9 Inequalities January 21, 2013

Example: Graph the following inequality

9 Inequalities January 21, 2013

Example: Graph the following system of inequalities.

9 Inequalities January 21, 2013

9 Inequalities January 21, 2013