Expressions, Equations, and Inequalities

is about...

understanding their similarities and differences

by

by

through

by

with

including

identifying expressions, equations,

and inequalities

translating expressions and equations

modeling equations

solving equations

solving and graphing inequalities

solving two-step equations

study extra hard!!

UNIT QUESTIONS:

You should be able to answer these by the time we complete this unit!!

1. When solving an equation or inequality, why is it important to perform identical operations on each side of the equal sign?

2. How can algebraic expressions and equations be written or translated?

3. How is solving an inequality similar to solving an equation, and how is different?

4. What is the difference between solving a one step equation and a two step equation?

Expressions, Equations, and Inequalities

COMPARE

unit words

CONTRAST

AND

previous unit

Properties &

Algebraic

Expressions

next unit

Ratios

&

Rates

Examples:

Numerical Expression

3(-4)

Algebraic Expression

( 3 + e ) - (-7)

Definition:

a name for a number

Numerical Expression:

includes at least ONE operation

Algebraic Expression

has a VARIABLE

Recognizing...

Equations

Examples:

3 + a = 6

4 + n = -5

2 + n = 7

Definition:

a math sentence that can include

NUMBERS

,

VARIABLES

(algebraic equation) and

AT LEAST ONE OPERATION

and

AN EQUAL SIGN

an equation means that two expressions are equal

Inequalities

Examples:

3 + 2 > 1 + 1

3 + x < 4

Definition:

a math sentence that includes

NUMBERS

,

VARIABLES

, and

AT LEAST ONE OPERATION

and states that

ONE EXPRESSION

is

GREATER THAN OR LESS THAN

the other expression

WHAT ON EARTH DOES THAT MEAN?

is

of

more than

less than

less

decreased by

MEANING...

subtract

multiply

subtract

subtract

add

equals

PRACTICING...

Inequalities

2x + 4 > 5

Don't forget to graph it!!

2x + 4 + (-4) > 5 + (-4)

(-2) + 2x > 1 + (-2)

x > -1

2(5) + 4 > 5

10 + 4 > 5

14 > 5

-1

0

1

2

Don't forget to check it!!

PRACTICING...

Equations

x + 2 = 8

x + 2 + (-2) = 8 + (-2)

x = 6

6 + 2 = 8

8 = 8

Don't forget to model it!!

Don't forget to check it!!

x

=

PRACTICING...

Expressions

4 + 2[3 x 5 + (8(3))]

4 + 2[3 x 5 + 24]

4 + 2[15 + 24]

4 + 2[39]

4 + 78

82

**THE END!!**

**use this as a study tool!!**

**Watch as many times as you need,**

**AND**

unit organizer