PRE-ALGEBRA

Lesson 2-8 Warm-Up

PRE-ALGEBRA What is an “inequality”? What is the “solution of an inequality”? How do you find all of the “solution of an inequality”? inequality (“in” means “not” and “equality” means “equal”): a number sentence that uses the inequality symbols >, <, ≥, or ≤ to show that the left side of the inequality symbol is or may be less than or greater than the right side. solution of an inequality: any number that makes the inequality true (Note: Usually, there will be an infinite number of solutions to an inequality.) Example: The “solutions of the inequality” x < 3 are all of the numbers that are less than 3. Tip: To find all of the solutions of an inequality, solve for the variable the same way you would if you were working with an “=“ sign by undoing operations until you have a variable on one side of the inequality sign and a number on the other. Then, graph the solutions on a number line. Inequalities and Their Graphs (2-8)

PRE-ALGEBRA An open dot shows that –2 is not a solution. A closed dot shows that –5 is a solution. Shade all the points to the right of –5. Shade all the points to the right of –2. Graph the solutions of each inequality on a number line. a. x > –2 b. w –5 > – Inequalities and Their Graphs LESSON 2-8 Additional Examples

PRE-ALGEBRA (continued) c. k 4 d. y < 6 < – A closed dot shows that 4 is a solution. Shade all the points to the left of 4. An open dot shows that 6 is not a solution. Shade all the points to the left of 6. Inequalities and Their Graphs LESSON 2-8 Additional Examples

PRE-ALGEBRA Write the inequality shown in each graph. a. b. x –3 > – x < 3 Inequalities and Their Graphs LESSON 2-8 Additional Examples

PRE-ALGEBRA How do you turn a written inequality into a graph? How do you turn a graph into a written inequality? Note: You can also write -1 ≥ a as a ≤ -1. Inequalities and Their Graphs (2-8)

PRE-ALGEBRA How do you write an equality from a word problem? To write an equality, from a verbal description, write the equality in words and then translate the words into an inequality. Example: Write an inequality for “The price is more than $4”. The inequality is p  4. The graph of the inequality is shown below. Inequalities and Their Graphs (2-8)

PRE-ALGEBRA Food can be labeled very low sodium only if it meets the requirement established by the federal government. Use the table to write an inequality for this requirement. LabelDefinition Sodium-free foodLess than 5 mg per serving Very low sodium foodAt most 35 mg per serving Low-sodium foodAt most 140 mg per serving Inequalities and Their Graphs LESSON 2-8 Additional Examples

PRE-ALGEBRA (continued) = 35 mg sodium Words number of milligrams of sodium in a serving of very low sodium food. v has at most a serving of very low sodium food Let Inequality 35v < – Inequalities and Their Graphs LESSON 2-8 Additional Examples

PRE-ALGEBRA x > –30 1.Graph –7 w. 2.Write an inequality for the graph. 3.A child must be at least 50 in. tall to ride on the roller coaster. Write an inequality for this situation. > – h 50 > – Lesson Quiz Inequalities and Their Graphs LESSON 2-8