1. Linear Inequalities Lesson 2.4

2. 2 Inequalities Definition 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 Note that each of these can be changed into the form ax + b § 0 where the § is the required inequality symbol

3. 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 <

4. 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. 5 Try It Out Given Graph each side of the equation Find intersection Decide which side of the intersection matches

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

7. 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. Assignment Lesson 2.4A Page 142 Exercises 1 – 73 EOO 8

9. 9 Compound Inequality Definition: Two inequalities connected by the words and or or Examples Anything in this format should be considered an " and " compound inequality

10. 10 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 [ )

11. 11 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

12. 12 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

13. Try It Out Temp in Fahrenheit x miles above ground level given by T(x) = 85 – 19x Use intersection of graphs to determine when temp is < 32  F What does x-intercept on graph y = T(x) represent? 13

14. Linear Regression Home ownership rates given by table Determine a linear modeling function Estimate years when ownership percent was between 58% and 60% Do we interpolate or extrapolate? 14 x1900195019802006 P47%55%64%69%

15. 15 Assignments Lesson 2.4B Page 144 Exercises 83 – 99 EOO