1. Chapter 4 Lesson 1 Inequalities and their Graphs

2. Objectives and Standards Objectives 1.Identify solutions of inequalities 2.Graph and write inequalities Standards 1. M11.D.1.1.3

3. Vocabulary Inequality – is a range of values identifiable by (greater than), ≦ (less than OR equal to), and ≧ (greater than OR equal to) instead of an equal sign (which denotes an equation) A solution of an inequality is any value or values of a variable in the inequality that makes the inequality true

4. Identifying Solutions by Evaluating Is each number a solution of 3 + 2x < 8? a)-2 b) 3 3 + 2(-2) < 8 Substitute in for x 3 + 2(3) < 8 3 – 4 < 8 Simplify 3 + 6 < 8 -1 < 8 Compare 9 < 8 -2 is a solution 3 is not a solution

5. Try on your own Is each number a solution of 2 – 5x > 13? a) 3 b) -4

6. Quick Check 1. Is each number a solution of x ≧ -4.1? a)-5 b) -4.1 c) 8 d) 0 2. Is each number a solution of 6x -3 > 10? a) 1 b) 2 c) 3 d) 4

7. Graphing Inequalities Graphing > OR < - To graph either less than or greater than, you must plot the point as an OPEN circle to show it does not include that point. Then color in the correct direction Graphing ≦ OR ≧ - To graph either less than OR equal to or greater than OR equal to, you must plot the point as a CLOSED circle to show that it does include the point. Then color in the correct direction.

8. Graphing Inequalities Graph the Inequalities a)d < 3 the solutions of d < 3 are all to the left of 3 b) -3 ≧ g The solutions of -3 ≧ g are -3 and all the points to the left of -3 123450 -2012-4-3

9. Example Try on your own Graph each Inequality a)c > 2 b)4 ≦ m

10. Writing an Inequality from a graph a) x < 2 Numbers are less than 2 are graphed b) x ≦ -3 Numbers equal to OR less than -3 are graphed 123450 -2012-4-3

11. Quick Check 2.Graph each inequality a)a < 1 b)n ≧ -3 c) 2 > p

12. Try on your own 3. Write an inequality for each graph a) b)