Writing & Graphing Inequalities Learning Target: Today I am learning how to write and graph inequalities on the number line because I want to be able to represent situations that have more than one correct answer.

An inequality is a mathematical sentence that has an inequality in it. Dr. Burger helps us write inequalities

Where might I see inequalities in real life?

If it’s any smaller, you’ve got to throw him back!

Practice Together You are going to Six Flags as soon as school is out (yaay!). You have to be at least 4 ft. tall to ride some of your favorite rides, but it isn’t only 4-foot tall people who can ride the rides! How tall can you be and ride the rides? See if you can figure out how to represent this with an inequality sign and a variable. (Hint: if it were an equation it would look like this: x = 4 ft. Use one of the inequality symbols posted on the board to make it an inequality.) What are the possible solutions for x (the variable)? 4 ft. tall and taller x > 4 ft. 4’, 4’1”, 4’2” . . . 6’, 6’1”, etc.! And everything in between!

What are some other situations that have more than one answer or qualifying response? Examples: Scores that qualify for an A: > 90 Money you need to get into Six Flags: > $39 Age required to get the kids’ meal: < 10 years old) Number of days to complete your project < 5 days

Inequalities 12-4 An inequality states that two quantities Course 2 12-4 Inequalities An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols: Symbol Meaning Word Phrases < > ≤ ≥ is less than Fewer than, below is greater than More than, above is less than or equal to At most, no more than is greater than or equal to At least, no less than

And: Symbol Meaning Word Phrases ≠ is not equal to Is not equal to

An inequality that contains a variable is an algebraic inequality An inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality. An inequality may have more than one solution. Together, all of the solutions are called the solution set.

Write an inequality for each situation. A. There are at least 15 people in the waiting room. “At least” means greater than or equal to. number of people ≥ 15 or x ≥ 15 B. The tram attendant will allow no more than 60 people on the tram. number of people ≤ 60 or x ≤ 60 “No more than” means less than or equal to.

Inequalities 12-4 Check It Out: Example 1 Course 2 12-4 Inequalities Check It Out: Example 1 Write an inequality for each situation. C. There are at most 10 gallons of gas in the tank. “At most” means less than or equal to. gallons of gas ≤ 10 or x ≤ 10 D. There are at least 10 yards of fabric left. “At least” means greater than or equal to. yards of fabric ≥ 10 or x ≥ 10

Graphing Inequalities Words aren’t enough. I want to show an inequality on a number line. Can I do that?? Dr. Burger says yes! We can graph inequalities

Course 2 12-4 Inequalities You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle. To indicate that solutions include numbers with values less than the point graphed, shade to the left of the point. To show that solutions include numbers greater than the point graphed, shade to the right of the point.

Inequalities 12-4 a > 5 b ≤ 3 Course 2 12-4 Inequalities This open circle shows that 5 is not a solution. a > 5 If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle. This closed circle shows that 3 is a solution. b ≤ 3

Symbols Review Open Circle Closed Circle The number is not included in the solution. The number is included in the solution.

Additional Example 2: Graphing Simple Inequalities Course 2 12-4 Inequalities Additional Example 2: Graphing Simple Inequalities On your own paper, graph each inequality. A. n < 3 3 is not a solution, so draw an open circle at 3. Shade the line to the left of 3. –2 –1 0 1 2 3 B. a ≥ –4 –4 is a solution, so draw a closed circle at –4. Shade the line to the right of –4. –6 –4 –2 0 2 4 6

Inequalities 12-4 Check It Out: Example 2 Course 2 12-4 Inequalities Check It Out: Example 2 On your own paper, graph each inequality. A. p ≤ 2 2 is a solution, so draw a closed circle at 2. Shade the line to the left of 2. –3 –2 –1 0 1 2 3 B. e > –2 –2 is not a solution, so draw an open circle at –2. Shade the line to the right of –2. –3 –2 –1 0 1 2 3

Insert Lesson Title Here Course 2 12-4 Inequalities Insert Lesson Title Here Ticket Out the Door Graph the inequalities on your own paper. 1. x > –1 º 1 2 3 – º 1 2 3 – 3. x < –1