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Evaluating Algebraic Expressions with exemples

Each algebraic expression consists of a series of numbers, variables, four operations, parentheses and other mathematical symbols.

Each variable can be replaced by a known number while keeping the same form of the expression. This process is called evaluating an expression, i.e. calculating its value by giving each unknown a certain value

In this section we will evaluate algebraic expressions for given values of the variables contained in the expressions. Here are some simple tips to help you be successful.

Note:

  1. Replace all occurrences of variables in the expression with open parentheses. Leave room between the parentheses to substitute the given value of the variable.
  2. Substitute the given values of variables in the open parentheses prepared in the first step.
  3. Evaluate the resulting expression according to the Rules Guiding Order of Operations.

Let's take some examples to make the idea clear.

Example1:

Evaluate the expression at .

Solution:

Following the tips above, first we replace all occurrences of variable in the expression with open parentheses.

Example2:

Evaluate the expression at .

Solution:

Following the tips above, first we replace all occurrences of variable in the expression with open parentheses.

Example3:

Evaluate the expression at .

Solution:

Following the tips above, first we replace all occurrences of variable in the expression with open parentheses.

Example4:

Evaluate the expression at .

Solution:

Following the tips above, first we replace all occurrences of variable in the expression with open parentheses.

Example5:

Evaluate the expression at .

Solution:

Following the tips above, first we replace all occurrences of variable in the expression with open parentheses.

Example6:

Evaluate the expression at .

Solution:

Following the tips above, first we replace all occurrences of variable in the expression with open parentheses.

Example7:

Evaluate the expression at and .

Solution:

Following the tips above, first we replace all occurrences of variable in the expression with open parentheses.