Vocabulary Inequality: A mathematical sentence that compares the values of two expressions using an inequality symbol. Solution of an inequality: any number that makes the inequality true. Example: the solutions of the inequality x < 3, are all numbers that are less than 3.

Is each number a solution of x 5? ALGEBRA 1 LESSON 3-1 > Yes, 5 5 is true. > No, –2 5 is not true. > Yes, 10 5 is true. > a. –2b. 10 c Inequalities and Their Graphs 3-1

ALGEBRA 1 LESSON 3-1 Is each number a solution of 3 + 2x < 8? a. –2b x < 8 –2 is a solution (–2) < 8Substitute for x. 3 – 4 < 8Simplify. –1 < 8 Compare x < 8 3 is not a solution (3) < 8 Substitute for x < 8 Simplify. 9 < 8Compare. Inequalities and Their Graphs 3-1

Tip: Always make sure the variable is on the left before you graph….. Because…….. Your solutions…….. (are you ready???????) Will always be…….. in the direction……… your inequality……… is pointing…… ****This is why we always SWITCH and FLIP!!!

Graphing Inequalities Since the solution of an inequality is not just one number, you can use a graph to indicate all of the solutions. Inequality Graph x<3 m > > a *switch (variable and number) and flip (inequality) first* will explain on next slide *The open dot shows that 3 is not a solution. Shade to the left of 3. *The closed dot shows that -2 is a solution. Shade to the right of -2 *The closed dot shows that -1 is a solution. Shade to the left of -1.

a. Graph d < 3. ALGEBRA 1 LESSON 3-1 b. Graph –3 ≥ g. The solutions of d < 3 are all the points to the left of 3. The solutions of –3 g are –3 and all the points to the left of –3. > Inequalities and Their Graphs 3-1

Write an inequality for each graph. ALGEBRA 1 LESSON 3-1 x < 2Numbers less than 2 are graphed. x > –2Numbers greater than –2 are graphed. x –3Numbers less than or equal to –3 are graphed. < Inequalities and Their Graphs 3-1 > x Numbers greater than or equal to are graphed

ALGEBRA 1 LESSON 3-1 Define a variable and write an inequality for each situation. a. A speed that violates the law when the speed limit is 55 miles per hour. b. A job that pays at least $500 a month. Let v = an illegal speed. The speed limit is 55, so v > 55. Let p = pay per month. The job pays $500 or more, so p 500. > Inequalities and Their Graphs 3-1

ALGEBRA 1 LESSON 3-1 Inequalities and Their Graphs pages 136–139 Exercises 2.no 4.yes 6.yes 8.yes 10.a. yes b. no c. yes 12. a. yes b. no c. no 14.a. no b. no c. yes 16.B 18.A

ALGEBRA 1 LESSON Is each number a solution of x > –1? a. 3b. –5 2.Is 2 a solution of 3x – 4 < 2? 3.Graph x > 4. 4.Write an inequality for the graph. 5.Graph each inequality. a. t is at most 2.b. w is at least 1. yesno p –2 < Inequalities and Their Graphs 3-1

Answers: Check your answers and turn in please. 4. Yes 10(a). Yes 12(b). No 14(c). Yes 16. B 20. O 23. O 28. X ≤ X < -1/2 34. a ≥