1. Linear Inequalities
Lesson 2.4

2. Inequalities Definition Examples Start with an equation 3x + 5 = 17
Replace the equals sign with one of
Examples
Note that each of these can be changed into the form ax + b § 0
where the § is the required inequality symbol

3. Solving Inequality in One Variable – Symbolic Method
Treat inequality in similar manner as an equation
Add same thing to both sides of inequality
Multiply both sides by same positive value
If negative value used, inequality reverses
Try it!
Inequality remains same
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4. Intersection of Graphs Method
Given f(x) > g(x)
Graph both f(x) and g(x)
Find the point of intersection
The solution set includes the x-values where f(x) is above g(x) •
f(x)
g(x)

5. Try It Out Given Graph each side of the equation Find intersection
Decide which side of the intersection matches

6. X-Intercept Method Write the inequality as h(x) < 0 Graph y = h(x)
Solutions occur where graph is below x-axis

7. Numerical Method Write the inequality as h(x) < 0
Place h(x) in Y= screen
Use Tables (♦Y) and observe values of x where the function is less than 0

8. Compound Inequality
Definition: Two inequalities connected by the words and or or
Examples
Anything in this format should be considered an "and" compound inequality

9. Solving Compound Inequality
Symbolically
Add the same thing to each part
Multiply each part by same positive number
Justify each step in the sequence to the right

10. Solving Compound Inequality
Graphically
Graph all three parts of the inequalities as functions
The solution will be the values of x for which the middle function is between the other two

11. Interval Notation Solution displayed in interval notation [-1, 2)
The [ or ] means that the number is included in the interval
The ( or ) means that the endpoint is not part of the interval [ )

12. Assignments Lesson 2.4A Page 118 Exercises 1 – 31 odd Lesson 2.4B