Algebra I CoursE. Lesson 2: Evaluating Expressions

Evaluating Expressions Variables can take multiple values. The evaluation process is one of the most difficult to grasp. I will make it as simple as replacing numerical values where the variables are present. In the future, those replacements (Evaluations) will use not only numerical values but algebraic expressions.

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1.2

Examples Suppose that in the following expression:

2x + 1

x=9

what is the final value of the expression?

Answering this question is not more than evaluating the expression Substitute the x by its value as follow:

2(9) + 1 = 19 2.9

Mathematical Structures 2(9) + 1 = 19 Structures are an essential part of understanding math. Evaluation, replacement, or substitution is the primary idea that will produce another math structure: equations.

3.3

The Parenthesis

()

This is a powerful structure within the math language structure.

The primary purpose is to show separation and imply a hidden operation.

4

3() This is basically the syntax. The hidden operation is multiplication by 3.

In another example,

()4

The structure implies separation, the base of the power expression that will later be a repeated multiplication.

5.5

More examples Evaluate for :

2

2x + 3x − 1 −3x + 2y 2 − hxy ax 2 + 8yh − h 5

a = −1 x=4 y = −5 h = 12 6.9

2

2x + 3x − 1

x=4

2

2(4) + 3(4) − 1 = Order of operations to solve exponents first

2(16) + 12 − 1 = 32 + 12 − 1 = 43

multiplication

left to right

7.10

2

−3x + 2y − hxy 2

−3(4) + 2(−5) − 12(4)(−5)

x=4

−12 + 2(25) − 12(4)(−5)

y = −5

−12 + 50 − 48(−5)

h = 12

38 + 240 = 278 8.12