9 solving inequalities
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9 Inequalities January 21, 2013
9 Inequalities
9 Inequalities January 21, 2013
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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
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