Algebraic Expressions Combination of variables and numbers using the

operations of addition, subtraction, multiplication, division, powers, or roots.

Variable: letter that represents a variety of numbers

Ex. x can represent diagonal length of a TV. Best distance to view image is 2.5 times diagonal length: 2.5x

Evaluating Algebraic Expressions Finding the value of the expression for a given value of

your variable.

Ex. What is the ideal distance away from a TV if the diagonal length is 60 inches (x = 60)?

2.5(60) = 150 inches

Evaluating Algebraic Expressions Evaluate:

1)

Evaluating Algebraic Expressions Evaluate:

2)

Evaluating Algebraic Expressions Evaluate:

3)

Formulas and Mathematical Models Equation: equal sign between two algebraic expressions

Formula: an equation that uses variables to express a relationship between two or more quantities

Ex. Formula that shows relationship between your age and your heart rate:

Light Exercise Intense Exercise

Formulas and Mathematical Models Mathematical Modeling: the process of finding

formulas to describe real-world phenomena.

Mathematical Model: Formula that is constructed by the process of mathematical modeling.

Ex. Heart rate formulas are mathematical models:

ages 19-30 represents group 4

Find F when x =4:

Actual calories: 2000

Conclusion: Model underestimates by 76 calories

Algebraic Expressions3x – 6y + 2

Terms: parts separated by addition/subtraction

3x, -6y, 2

Coefficient: number in front of terms

3, -6, 2

Constant Term: term consisting of only a number

2

Like Terms: terms with same variable factor

7x and -2x are Like Terms

Properties of Real Numbers

Simplifying an Algebraic Expression Note: We can combine like terms using the properties

of real numbers. For example: 7x – 2x = 5x

Ex. Simplify:

1)

2)

3)

Practice ProblemsPage 347

Evaluate Expression: #5, 9, 13, 19, 22, 31, 33

Formulas: #35, 36, 37, 38

Simplify Expression: #41, 49, 55, 57, 59

Applications: #67, 68, 70, 71, 72