6EE. 8 INEQUALITIES Expressions and Equations!

Objectives! Content  Graph inequalities

Questions! Answers! Simplify: 3(y + 2) = n+n+n+n = Is 4n +3n^2 equivalent to 7n^3? Expand:12y + 24 = 12( + ) 3x = Solve: x 7 + n 3 when n is 3 3y + 6 4n 12(y + 2) x + x+ x 119 Review!

Questions! Answers! What is the inverse of each of the following operations? Addition Multiplication Subtraction Division Subtraction Division Addition multiplication Solve Equations Speed Review

Questions Answers What does it mean to isolate the variable? How do we isolate the variable? Solve X + 2 = 5 4x = 12 T – 5 = 11 z divided by 5 = 1 To get the variable on one side of the equal side alone. By performing the inverse operation. X = 3 T = 16 Z = 1 Solve Equations Speed Review!

Inequalities! What does the word inequality mean to you? What does it remind you of? What does it mean?

Inequalities! An inequality is a relation between two expressions that is expressed by placing an inequality symbol between the two expressions. Inequalities have solutions. A solution to an inequality is any value of the variable that makes the inequality true.

How to Read Inequalities! > = greater than < = Less than = means equal What symbol could you use for not equal? What symbol could you use if something is equal or greater? What symbol could you use if something is equal to or less than?

Inequalities How to Read… Let’s read the following inequalities out loud together A > 4 a < 4 a = 4 A > 4 a < 4 How would you read this inequality? 5 < a < 8 How would you read this symbol? = “A is greater than 4” “ A is less than 4” “A is equal to 4” “A is greater than or equal to 4” “ A is less than or equal to 4” “A is greater than 5 and less than 8” “Not equal to” How to Read Inequalities!

Graphing Inequalities Basic inequality signs < Less than > Greater than ≤ Less than or equal to ≥ Greater than or equal to

Graphing Inequalities X < 4 X > -2 X ≤ - 4 X ≥ 3

Graphing Inequalities > X < ≤ X ≥ ≥ X ≤ 5

Graphing Inequalities Partner Activity > X < ≤ X ≥ ≥ X ≤

Objectives Day 2 Read and write inequalities

1) Write an inequality to represent all numbers on a number line to the right of -4 1/2 and to the left of or equal to 7. Let x represent the numbers. -4 ½ < x < 7

at least 1 piece and as many as 3 pieces of pizza 1 < x < 3

Colleen spent somewhere between $2.50 and $3.00 on stamps. $2.50< x < $3.00

Margaret spends at least $19.00 but she can’t spend more than $ Write an inequality to show how much money she has. x< $25.00

Numbers that are less than or equal to 1 x< 1

Numbers that are greater than -3 and less than or equal to zero. -3 < x < 0

Numbers that are greater than 4 or less than < x < -2

Solving Inequalities If T represents the temperature, then the inequality 13 < T < 29 represents normal January temperatures in Chicago. What temperatures are solutions to this inequality? A solution makes the inequality true. How can you figure out the solution/s?

Solving Inequalities! It is easy to find the solution/s for inequalities by graphing them on a number line. If the sign is greater or less than, draw an open circle over the number. If the sign is greater than or equal to or less then or equal to, color in the circle. Draw a line from the number in the direction that represents if the variable is greater than or less than.

Let’s Practice! 13 < T < 29

Let’s Practice! R < 1 g > -3

Let’s Practice! -3 < t < 0.5 < d < 4

Practice! Inequalities “Guess Who” with a partner. Inequalities Matching on your own Homework: Enrichment 23.5

n + 3 > 8 n – 5 < 1 n + 3 < 5 n – 2 > 2 -8 < -4x < 12 0 < x- 2 < 7