6 3 Introduction to Linear Inequalities Inequalities We

6. 3 Introduction to Linear Inequalities

Inequalities • We can use an inequality to model a situation that can be described by a range of numbers instead of a single number. • These are the symbols we will be using…

What inequalities that represent these situations?

Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly < less than > greater than Notice open circles

Example 2 3 4 5 6 7 8

Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly ≤ less than or equal to ≥ greater than or equal to Notice colored in circles

Inequalities and their Graphs Let’s work a few together Notice: when variable is on left side, sign shows direction of solution -2 Color in circle

What inequalities represent these situations? What is the difference between an open and a closed circle?

Graph each of the following on a number line.

Possible solutions to the Inequality?

Solving Inequalities using Addition/Subtraction • Solving inequalities follows the same procedures as solving equations. • The final solution is what you GRAPH.

Solve the inequality: x+4<7 -4 -4 x < 3 ●Subtract 4 from each side. ●Keep the same inequality sign. ●Graph the solution. • Open circle, line to the left. 0 3

How to graph the solutions > Graph any number greater than. . . open circle, line to the right < Graph any number less than. . . open circle, line to the left Graph any number greater than or equal to. . . closed circle, line to the right Graph any number less than or equal to. . . closed circle, line to the left

Assignment Time! #3 • Page 292: 6 a, 9, 12 • Page 298: 4 ace, 7, 8 ace • WRITE THE ORIGINAL INEQUALITY IN YOUR BOOK AND… • MAKE SURE YOU SHOW ALL STEPS!!