Review of 9.1-9.5. Definitions.

Review of 9.1-9.5

Definitions• Numerical expression: string of numbers and operation symbols (exponents, not including =) and possibly grouping symbols


• Ex:


• Ex:

• (Algebraic) expression: numerical expression which also may include variables (symbols that stand for any number in a specified set of values)


• Ex:


• Ex:


• Ex:


• Ex:

• Equivalent expressions: evaluate to be the same value for all possible choices of values for the variables


• Ex:


• Ex:


• Ex’s: and


• Ex:


• Ex:


• Ex’s: and

• Equation: statement that 2 expressions and/or numbers are equal


• Ex:


• Ex:


• Ex’s: and

• Equation: statement that 2 expressions and/or numbers are equal• Ex:


• Ex:


• Ex:


• Ex’s: and

• Equation: statement that 2 expressions and/or numbers are equivalent• Ex:

• Identity: an equation which is true for all values of the variables


• Ex:


• Ex:


• Ex’s: and

• Equation: statement that 2 expressions and/or numbers are equivalent• Ex:

• Identity: an equation which is true for all values of the variables• Ex:

Example problem

Ex: Find an expression for the area of a room with the following floor plan?

d

a

b

c

Solving Equations

How can we change an equation without changing the solutions?

Solving Equations

How can we change an equation without changing the solutions?1) Use properties of arithmetic to simplify the expression on one side

of the equation

Solving Equations


of the equation2) Add/subtract the same quantity (can include variables) to both

sides of the equation

Solving Equations


of the equation2) Add/subtract the same quantity (can include variables) to both

sides of the equation3) Multiply/divide the same nonzero quantity (can also include

variables*) on each side of the equation

Other example problems

• See activity 9T, problems 1, 2, and 4• See activity 9W, problems 1 and 2

Review of 9.1-9.5. Definitions.

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