Linear Inequalities Lesson 2 4 Inequalities l Definition

Linear Inequalities Lesson 2. 4

Inequalities l Definition l l l Start with an equation 3 x + 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 2

Solving Inequality in One Variable – Symbolic Method l Treat inequality in similar manner as an equation l l Add same thing to both sides of inequality Multiply both sides by same positive value If negative value used, inequality reverses Inequality remains same < Try it! 3

Intersection of Graphs Method l l l Given f(x) > g(x) Graph both f(x) and g(x) Find the point of intersection • f(x) l The solution set includes the x-values where f(x) is above g(x) 4

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

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

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

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

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

Solving Compound Inequality l Graphically l l 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 10

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

Assignments l l l Lesson 2. 4 A Page 118 Exercises 1 – 31 odd Lesson 2. 4 B Page 120 Exercises 33 – 75 odd 12