ALGEBRA READINESS LESSON 9-1 Warm Up Lesson 9-1 Warm-Up

ALGEBRA READINESS LESSON 9-1 Warm Up Lesson 9-1 Warm-Up

ALGEBRA READINESS “Writing Inequalities” (9-1) 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 tha 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.

ALGEBRA READINESS 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. “Writing Inequalities” (9-1)

ALGEBRA READINESS “Writing Inequalities” (9-1) 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.

ALGEBRA READINESS a.) Is each number a solution of x 5? > Yes, (5) 5 is true. > No, (–2) 5 is not true. > Yes, (10) 5 is true. > a. –2 b. 10 c Writing Inequalities LESSON 9-1 Additional Examples

ALGEBRA READINESS b.) Write an inequality for the verbal description. “The distance d is more than 90 feet.” The inequality is d > 90. The graph of the inequality is shown below. Inequality d > 90 Wordsd is more than 90 Writing Inequalities LESSON 9-1 Additional Examples

ALGEBRA READINESS “Writing Inequalities” (9-1) What is a “system of inequalities”? How do you write a system of inequalities? System of Inequalities: two or more inequalities done together To write a system of inequalities, write both inequalities using the same variable. Example: During a recent storm, the wind speed was greater than 52 mi./ hr. but less than 75 mi./hr. Write a system of inequalities to represent this situation.

ALGEBRA READINESS Let a = a patient’s age. A health insurance company offers a special plan for patients who are at least 30 years old and less than 55 years old. Write a system of inequalities for this situation. age is less than 55 years: a < 55 age is at least 30 years: a 30> – The system is. a 30 > – a < 55 Writing Inequalities LESSON 9-1 Additional Examples

ALGEBRA READINESS Students who bring 3.5 pounds or more of recyclable aluminum get into the Environment Dance free. Which students can attend free: Ben (3.35 lb), Rinaldo (2.75 lb), Juanita (3.75 lb)? > – Wordsamount ofis equal to3.5 lbs aluminumor more than Let a = a person’s amount of aluminum. Inequality a 3.5 Writing Inequalities LESSON 9-1 Additional Examples Decide whether the inequality is true or false for each person. Ben false > – Rinaldo false > – Juanita true > – Juanita can attend the dance free.

ALGEBRA READINESS Write an inequality for each verbal statement. 1. A dog weighs less than 25 pounds. 2. You must be at least 18 to vote. 3. Tell which numbers are solutions of x ≥ – 4: – 6, – 4, –2, 0, 2. d < 25 – 4, –2, 0, 2 v ≥ 18 Writing Inequalities LESSON 9-1 Lesson Quiz