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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Examples

Suppose that in the following expression:

2x +1 x = 9

what is the final value of the expression? evaluating the expression

Answering this question is not more than

Substitute the x by its value as follow: 2(9)+1 = 19

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.

The Parenthesis  ()

This is a powerful structure within the math language structure.

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

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

In another example,

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

More examples

Evaluate for :

2x + 2 3x −1

−3x +2y − 2 hxy

a = −1

+ 5 ax 8yh − h2

x = 4

y = −5

h = 12

2x + 2 3x −1 x = 4

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

exponents first multiplication

−3x +2y − 2

−3(4)+2(−5) − 2 12(4)(−5)

−12+2(25)−12(4)(−5)

−12+50−48(−5)

38+240 = 278

x = 4 y = −5 h = 12