Unit 6- Inequalities
This unit is about solving inequalities and displaying solutions on a number line.
Solving Inequalities
Definitions-
- __> = Greater than or equal to.
- > = Greater than.
- __< = Less than or equal to.
- < = Less than.
-The unknown variable can have more than one value. For example, in the inequality 2x < 9, x could equal many numbers. It could equal 2, 3 or 4, but could also equal 2.56 or 3.2134787462847682654958409578364872846546975096789636458365.
-If the number is negative, then switch the inequality sign around.
Example- -2x < 4 turns into x > -2.
-The boundary point is the number that will make the two sides of the inequality equal each other. To find it, simply solve the equation.
Example- 3x -2 __< 10
3x -2+2 __ < 10+2
3x __ < 12 The boundary point is 4.
3x / 3 __< 12 / 3
x __< 4
-When multiplying or dividing by a negative number in the last step, remember to switch the sign to it's opposite.
-If the number is negative, then switch the inequality sign around.
Example- -2x < 4 turns into x > -2.
-The boundary point is the number that will make the two sides of the inequality equal each other. To find it, simply solve the equation.
Example- 3x -2 __< 10
3x -2+2 __ < 10+2
3x __ < 12 The boundary point is 4.
3x / 3 __< 12 / 3
x __< 4
-When multiplying or dividing by a negative number in the last step, remember to switch the sign to it's opposite.
Putting Solutions on a Number Line
-When putting numbers on a number line, use dots to signify the sign. A white dot means that the sign is a < or >. A black dot means that the sign is a __< or __>.