Linear Inequalities
In this chapter you will learn to represent linear inequalities verbally, algebraically, and graphically, to determine and verify solutions of linear inequalities, to generalize and apply rules for solving linear inequalities, to compare and explain the processes for solving linear equations and linear inequalities, to compare and explain solutions of linear equations and linear inequalities, and to solve problems involving linear inequalities.
![Picture](/uploads/2/8/6/5/28654915/3393525.png)
Boundary Point:
-Is the number that will make the two side of the linear inequality equal to each other.
-The boundary point is the Lowest number you can have that would = the answer and make the equation equal. The boundary point is always the variable.
-Is the number that will make the two side of the linear inequality equal to each other.
-The boundary point is the Lowest number you can have that would = the answer and make the equation equal. The boundary point is always the variable.
![Picture](/uploads/2/8/6/5/28654915/262346.png)
The rules change if you multiply or divide by a (-)number: reverse inequality sign.
![Picture](/uploads/2/8/6/5/28654915/5397557.png)
Solve for the inequalities:
In this case you will take out the number with the variable by cancelling it out and what you do to one side you will do to the other, so subtract or add the number. After that you should have an (x), a (< or >) and the number that was subtracted or added for the answer.
In this case you will take out the number with the variable by cancelling it out and what you do to one side you will do to the other, so subtract or add the number. After that you should have an (x), a (< or >) and the number that was subtracted or added for the answer.
![Picture](/uploads/2/8/6/5/28654915/606048.png?325)
Graphing the inequalities
Solve the same way but now graph the answer. When you are graphing and you have a greater than or equal to OR less than or equal to the the circle will be filled in but if it is just greater than or less than then the circle will be open. Also the direction of the arrow will be determined by the way that the sign is going.
Solve the same way but now graph the answer. When you are graphing and you have a greater than or equal to OR less than or equal to the the circle will be filled in but if it is just greater than or less than then the circle will be open. Also the direction of the arrow will be determined by the way that the sign is going.