Graphing Equations and Inequalities

PODDistribute1) 5(-6b + 6)2) -6(4r – 4)Combine Like Terms3) -30x + 30 + 5xSolve4) 5v + 5(-6v + 6) = -6(4v – 4)

5v + 5(-6v + 6) = -6(4v – 4)

Essential Questions:What is an inequality?

How can I graph solutions of equations and inequalities on a number line?

Let’s Graph the Solution to an equation on a Number Line!

Number lines are used to graph some solutions.

x + 3 = -1x + 3 -3 = -1 -3 x = - 4

We already found thesolution to this equation.

Now, what does it mean on a number line?

If we say that “a variable = a number”, that is where we place the

point on the number line!

Example:

If we say that “a variable = a number”, that is where we place the

point on the number line!

Example:

0 1 2 3 4 5 6-1-2-2-3-4-5-6

X = -3

What Is The Difference Between Equalities And Inequalities?

The only difference is the number of solutions!

The only difference is the number of solutions!

• An equality gives one definite solution.

• An inequality give a set of solutions!

Inequality Symbols

< Less Than x < 5

> Greater Than x > 5

< Less Than OR Equal to x < 5

> Greater Than OR Equal to x > 5

If we say that x > 6, aren’t we stating that x can be

any amount greater than 6?

What are some examples??

How Do We View A Set Of Solutions On A Number Line?

Let’s find out!

When graphing inequalities, we must show where to begin the set of solutions and where they continue on the number line.

For example:

r < 1

0 1 2-1-2

Use an open dot

When graphing inequalities, we must show where to begin the set of solutions and where they continue on the number line.

For example:

r > 1

0 1 2-1-2

Use a closed dot

If you noticed, some number lines had filled in circles

and others did not.

What do you think was the reason?

The filled in circle shows that the designated number is

included in the solution set.This is shown with < or >.

X < -4

The unfilled circle shows that the designated number is not

included in the solution set.This is shown with < or >.

X < -4

Inequality Symbols

< Less Than – Open Dot

> Greater Than – Open Dot

< Less Than OR Equal to – Closed Dot

> Greater Than OR Equal to – Closed Dot

Solve and Graph the Following on Your Paper:

A.) x – 1 > 5

B.) 4 + n < -1

C.) 5+ z > 10

D.) -15 + r < -14

A.) x - 1 > 5

B.) 4 + n < -1

C.) 5 + z > 10

D.) -15 + r < -14

A.) x - 1 > 5

B.) 4 + n < -1

C.) 5 + z > 10

D.) -15 + r < -14

0 1 2 3 4 5 6-1-2-2-3-4-5-6

0 1 2 3 4 5 6-1-2-2-3-4-5

0 1 2 3 4 5 6-1-2-2-3-4-5-6

0 1 2 3 4 5-1-2-2-3-4-5-6

You should have drawn these solutions:

On your paper, solve and graph the following:

A. 5 + n = 9

B. 19 + m > 5

C. -6 + b = 4

D. K - 17 < 14

E. 2d > 12

Now, Let’s Compare Equalities and Inequalities:

EqualitiesSolve by

performing the inverse operation

Only one definite solution

The solution is shown with one filled circle on a number line

InequalitiesSolve by

performing the inverse operation

A set of solutionsThe solution is

shown with a filled or unfilled circle with a line or line segment

One more difference…

-5 -5 5x < -25

5 5 x < -5

- 5 -5 -5x < 15 -5 -5 x > -3

When you multiply

OR

Divide

BY

A negative

flip the inequality

When you multiply

OR

Divide

BY

A Positive

the inequality stays the same

Vocabulary

• Number line

• Solution

• Inverse Operation

• Equality

• Inequality

Perform the inverse operation

to solve for a variable!

Remember: