Solving InequalitiesAddition and Subtraction.

Module 3, Lesson 3

Online Algebra

VHS@PWCS

Inequalities

Inequalities are statements that use the following symbols (the symbol points to the smaller quantity):

> - Greater than

< - Less than

> - Greater than or equal to

< - Less than or equal to

≠ - Not equal to

Graphing inequalitiesx > -1

Think of some values of x that fit this solution. How many values did you come up with?

You should have come up with several. Inequalities have an infinite number of solutions.

In this case anything less than -1 is a solution. Instead of points we use a line, to show that anything less than -1 is

included. We also use an open circle on -1 to show that numbers very close to -1

are included but not the -1

-6 -4 -2 0 2 4

Graph The Following Inequalities

x > -2

Remember that we use an open circle and a

line to graph this inequality.

x > -2

Because this inequality represents x is greater than or

equal to -2, -2 is part of the solution. To show this

graphically we use a closed circle.

-6 -4 -2 0 2 4

Solving Inequalities Solving inequalities are just like solving equations.

c + -13 = 7

Recall that to solve this equation we add 13 to

both sides.

c + -13 + 13 = 7 + 13

c = 20

c + - 13 < 7

To solve this inequality. We do the same thing, add

13 to both sides.

c + -13 + 13 < 7 + 13

c < 20

The only difference

is the graph of the

solution.

15 17 19 21 23 25

Solve and graph 4 > x - 121. Rewrite as addition.

4 > x + -12

2. Add 12 to both sides.

4 + 12 > x + -12 + 12

16 > x

3. If we flip the inequality it makes it easier to graph.

x < 16

11 13 15 17 19 21

Notice that “point” is still pointing to the x, when we flip.

This makes it easier to graph because if our x is on the left side of the inquality our line will go in the same direction as the symbol.

Solving Inequalities, A Recap

Solving inequalities is just like solving an equation.

To graph we use a line and either an open or closed circle.

Use an open circle with < or >. Use a closed circle with < or >.