Chapter Three:  Equations

Take notes on the following topics.

Chapter Three

Section 3.1

Section 3.2

Section 3.3

Section 3.4

Section 3.5

Section 3.6

Section 3.7

Section 3.8

Section 3.9

Section 3.10

Section 3.11

Section 3.12

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Section 3.1 : Addition Property of Equality

Vocabulary

• equivalent equation

• replacement set

• Addition Property of Equality

• Subtraction Property of Equality

Example

Given the equation                 x - 7 = 17

Add 7 to each side.          x - 7 + 7 = 17 + 7

Simplify.                                     x = 24

Check.                                  x - 7 = 17

Substitute 24 for x.                24 - 7 = 17

Simplify.                                   17  = 17 (true)

Thus, the solution is 24.

 

Subtraction Property of Equality

For all real numbers,  a, b,  and  c,  if a = b,  then  a - c = b - c. This means that subtracting the same number from each side of an equation produces an equivalent equation,

Example

Given the equation                                 x + 7 = -18 

Subtract 7 from each side.                x + 7 - 7 = -18 - 7

Simplify.                                                     x = -25

Check.                                                 x + 7 = -18

Substitute -25 for x.                            -25 + 7 = -18

Simplify.                                                   -18 = -18 (true)

Thus, the solution is -25.

Take class notes.

Before starting your homework, rework the examples that are illustrated in this section of your textbook and the examples that I demonstrated in class. 

Then do your homework.

Write down questions (examples or concept that you do not understand).......then.............. Ask these questions in class.