List at least two 2 similarities and at least two 2 differen

List at least two (2) similarities and at least two (2) differences between linear equations and linear inequalities.

Describe a situation that can be best modeled by an inequality statement and one that can be best modeled by an equation.

Think about the different ways in which linear relationships (equations and inequalities) are represented. What struggles do you have shifting between the different representations? Which representation(s) are more meaningful to you? What are the benefits of using multiple representations?

Solution

SIMILARITIES:-

1) Adding and subtracting the number from both sides.

2) Multiplying and dividing both sides by the positive number.

3)Applying an increasing functions from both sides.

4) Simplifying one or both sides.

DIFFERENCES:-

1)Multiplying or dividing both sides by a negative number changes the direction of an inequality. So we cannot multiply or divide both sides by a variable unless we know that the variable is either always positive or always negative. This is not a concern when solving equalities.

2)When applying a decreasing function to both sides of an inequality, the direction of the inequality changes.

3) Swapping both sides of an inequality also changes the direction of an inequality. Again we don\'t have to worry about this with equalities.

DEFINITION OF INEQUALITIES:-

Inequalities are math statements that define a range of values. They are easily recognizable because they contain the symbols <, , >, or

INEQUALITIES VS EQUATION BY USING EXAMPLE AND MODELS:-

Inequalities are different than equations, although you can apply what you know about equations to help you understand inequalities. Inequalities and equations are both math statements that compare two values.

An equation contains the symbol =, which links two expressions that have the same value. You are familiar with equations like these:

26 = 21 + 5

y = 3x + b

5t = 2(t + 3)

Even without solving them, you know that the quantity on the left-hand side of the equals sign has the same value as the quantity on the right-hand side of the equals sign.

Inequalities are different. In an inequality, one side of the inequality can be larger or smaller than the quantity on the other side. The math symbols <, , >, and provide information about the relative sizes of the two expressions.

Notation

How to Read It

Sample Inequality

x < y

“x is less than y”

3 < 15

x y

“x is less than or equal to y”

number of people present in class number of people enrolled in class

x > y

“x is greater than y”

9> 6

x y

“x is greater than or equal to y”

50 the number of stars on any United States flag

The important thing about inequalities is that there are multiple possible solutions. Note that the inequality x > y can also be written as y < x. The sides of any inequality can be flipped as long as the inequality symbol between them is also reversed.

LINEAR RELATIONSHIP BETWEEN EQUATION AND INEQUALITIES:-

An equation states that two expression are equal while inequalities relates two difeerent values.

key points:-

REPRESENTATION OF EQUATION AND INEQUALITY:-

Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used.

For example: 1) The equation 10x + 17 = 3x can be changed to 7x + 17 = 0, and then to 7x = -17 by adding/subtracting the same quantities to both sides. These changes do not change the solution of the equation.

2): Using the formula for the perimeter of a rectangle, solve for the base in terms of the height and perimeter.

Representation of inequalities:-

Solve linear inequalities using properties of inequalities. Graph the solutions on a number line.

For example: The inequality -3x < 6 is equivalent to x > -2, which can be represented on the number line by shading in the interval to the right of -2.

BENEFITS OF USING MULTIPLE REPRESENTATIONS:-

Multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties.

By using multiple representations between equation and inequality, we have an important benefit i.e

1)Understand the problem.

2)Give the meaning to the manipulatives.

Notation	How to Read It	Sample Inequality
x < y	“x is less than y”	3 < 15
x y	“x is less than or equal to y”	number of people present in class number of people enrolled in class
x > y	“x is greater than y”	9> 6
x y	“x is greater than or equal to y”	50 the number of stars on any United States flag