< > < < Writing Inequalities < < < >.

Slides:



Advertisements
Similar presentations
An Introduction to Inequalities
Advertisements

Halloween Warm up There are 25 students in my class. 17 said they would go trick or treating this year, 20 said they would go to a haunted house and 4.
3-1 Exploring Inequalities and Their Graphs
Objective: Students will be able to write and solve two- step equations with one variable!
Solving and Graphing Inequalities
Solving Inequalities Using Addition & Subtraction.
InequalitiesInequalities. An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: Inequalities work like equations,
Solving Two- Step Equations Lesson 2-2. Rules to Remember When solving an equation, the goal is to get the variable by itself. Addition and Subtraction.
Expression or Equation? 3x + 7 4y – 10 = 54 5z + 32 = 47 6x + 2y (8x – 1) 2 + y 2x = 16.
Solving Inequalities Using Addition & Subtraction.
Solving Inequalities 3-1 Exploring Inequalities and Their Graphs.
Winter Warm up There are 25 students in my class. 17 said they would go snow skiing this year, 20 said they would go to Universal Studios and 4 would not.
Solving two step Inequalities < < < > < > <
BY: KAYLEE J. KAMRYN P. CLOE B. EXPRESSIONS * EQUATIONS * FUNCTIONS * AND INEQUALITIES.
NUMBER SENTENCES 6.7.
Solving inequalities. An equation. Solve this and graph the answer on a number line: x - 2 = 5.
Equations and Inequalities. Unit 8 – Solving Inequalities.
Solving Two- Step Equations
< > < < Solving Inequalities < < < >.
Graphing and Solving Inequalities
< > < < Solving Inequalities < < < >.
Group Do Now Get on your mark You will need to pass out role cards
Using Multiplication & Division
< > < < < < < > Solving Inequalities
Problem Solving with Two-Step Equations
Solving Two- Step Equations
Objective 3.6 solve multi-step inequalities.
Solving Two- Step Equations
Warm-Up 13 x 3 14 x 4 12 x 11 9 x 13.
Using Addition & Subtraction
< > < < Inequalities < < < >.
Solving Two- Step Equations
< > < < < < < > Solving Inequalities
< > < < Solving Inequalities < < < >.
< > < < < < < > Solving Inequalities
Using Addition & Subtraction
Warm up Paul has two dozen cookies. He will eat three cookies on Sunday. On every day that follows, he will eat a number of cookies that is one greater.

Warm Up Graph each set of numbers on a number line. -3, 7, -9
Warm Up Graph each set of numbers on a number line. -3, 7, -9
Inequalities Objective: Students will be able to solve, graphing and write inequalities with one variable and apply them to real world situations.
One step equation with Multiplication and Division
Solving Two- Step Equations
Write & Solve Equations
Equation- a math sentence with an equal sign.
Two Step Equation.
Equation with variables on both sides
Stand Quietly.
One step equation with Addition and Subtraction
Solving and Graphing Inequalities
Using Addition & Subtraction
< > < < < < < > Solving Inequalities
Two step equation Operations
Solving Two- Step Equations
< > < < < < < > Solving Inequalities
Solving and Graphing Inequalities
Solving Inequalities.
< > < < Solving Inequalities < < < >.
Two step equation Brackets
Solving Inequalities Solving inequalities follows the same procedures as solving equations. There are a few special things to consider with.
Do Now Evaluate 9h + h if h = 2.1 Evaluate 2 (4 + g) 2 If g = 6.
Graphing Inequalities
Halloween Warm-Up Paul has two dozen Halloween cookies. He will eat three cookies on Sunday. On every day that follows, he will eat a number of cookies.
Involving One Operation
Using Addition & Subtraction
Agenda Ticket in the door Ticket in the door review
< > < < < < < > Solving Inequalities
1.3:Solving and Graphing Linear Inequalities
Objective: Write, Graph, and Solve Inequalities
Using Addition & Subtraction
Presentation transcript:

< > < < Writing Inequalities < < < >

≥ : greater than or equal to An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to

What do Inequalities mean? A mathematical sentence that uses one of the inequality symbols to state the relationship between two quantities.

Mathematics is not always about "equals" Mathematics is not always about "equals"! Sometimes we only know that something is bigger or smaller than something else.

Example: Alex and Billy have a race, and Billy wins! What do we know? We don't know how fast they ran, but we do know that Billy was faster than Alex: Billy was faster than Alex We can write that down like this: b > a (Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was)

Example: Alex plays in the under 15yr soccer. How old is Alex? We don't know exactly how old Alex is, because it doesn't say "equals" But we do know "less than 15", so we can write: a < 15 The small end points to "a" because the age is smaller than 15.

Example: you must be 13 or older to watch a movie. The "inequality" is between your age and the age of 13. Your age must be "greater than or equal to 13", which is written: Age ≥ 13

Graphing Inequalities < > < < Graphing Inequalities < < < >

Graphing Inequalities When we graph an inequality on a number line we use open and closed circles to represent the number. Plot an open circle < < ≤ ≥ Plot a closed circle

x < 5 means that whatever value x has, it must be less than 5. Try to name ten numbers that are less than 5!

Numbers less than 5 are to the left of 5 on the number line. 5 10 15 -20 -15 -10 -5 -25 20 25 If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right. There are also numbers in between the integers, like 2.5, 1/2, -7.9, etc. The number 5 would not be a correct answer, though, because 5 is not less than 5.

Try to name ten numbers that are greater than or equal to x ≥ -2 means that whatever value x has, it must be greater than or equal to -2. Try to name ten numbers that are greater than or equal to -2

Numbers greater than -2 are to the right of -2 on the number line. 5 10 15 -20 -15 -10 -5 -25 20 25 -2 If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right. There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5, etc. The number -2 would also be a correct answer, because of the phrase, “or equal to”.

Solving Inequalities

Solving an Inequality The goal is to get the variable by itself. Follow the same rules and steps that we used to solve an equation. USE OPPOSITE OPERATIONS TO UNDO. 1. Always undo addition or subtraction first, then multiplication or division Remember whatever is done to one side of the inequality must be done to the other side.

Solve an Inequality w + 5 < 8 - 5 -5 w < 3 - 5 -5 w < 3 All numbers less than 3 are solutions to this problem! 5 10 15 -20 -15 -10 -5 -25 20 25

More Examples 8 + r ≥ 12 -8 -8 r 4 All numbers greater than 4 (including 4) ≥ 5 10 15 -20 -15 -10 -5 -25 20 25

All numbers less than 8 (including 8) More Examples 2h + 8 ≤ 24 -8 -8 2h ≤ 16 2 2 h ≤ 8 All numbers less than 8 (including 8) 5 10 15 -20 -15 -10 -5 -25 20 25

More Examples 2x > 2 2 2 x > 1 2 2 x > 1 All numbers greater than 1 make this problem true! 5 10 15 -20 -15 -10 -5 -25 20 25

Your Turn…. x > 1 d > 4 x < 11 c < 3 x + 3 > 4 Solve the inequality and graph the answer. x + 3 > 4 6d > 24 2x - 8 < 14 2c – 4 < 2