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How do you evaluate algebraic expressions step by step?

Published in Algebraic Evaluation 2 mins read

Evaluating algebraic expressions involves substituting given numerical values for variables and then simplifying the resulting arithmetic expression. Here's a step-by-step guide based on the provided reference:

Steps to Evaluate Algebraic Expressions

The process consists of three key steps:

  1. Obtain the value of variables: The first step is to identify and note the numerical values assigned to each variable in the algebraic expression.

  2. Substitute the numerical value: Replace each variable in the expression with its corresponding numerical value.

  3. Simplify the arithmetic expression: Apply the order of operations (PEMDAS/BODMAS) to simplify the resulting numerical expression. This ensures you perform operations in the correct sequence: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Detailed Explanation with Examples

Let's break down each step with illustrative examples:

1. Obtain the value of variables

This step involves understanding what values are given for each variable in the problem. For instance:

  • If the problem states "Evaluate 2x + 3 where x = 5," then the value of the variable x is 5.

2. Substitute the numerical value

Next, substitute the obtained values into the algebraic expression. Continuing the example above:

  • Substitute x = 5 into 2x + 3 to get 2(5) + 3.

3. Simplify the arithmetic expression using the order of operations

Now, simplify the expression 2(5) + 3 using the correct order of operations:

  1. Multiplication: 2 * 5 = 10
  2. Addition: 10 + 3 = 13

Therefore, the value of the algebraic expression 2x + 3 when x = 5 is 13.

Example with Multiple Variables and Operations

Consider the expression 3a + b^2 - c, where a = 2, b = 4, and c = 1.

  1. Obtain values: a = 2, b = 4, c = 1

  2. Substitute: 3(2) + (4)^2 - 1

  3. Simplify:

    • Exponents: 4^2 = 16
    • Multiplication: 3 * 2 = 6
    • Addition: 6 + 16 = 22
    • Subtraction: 22 - 1 = 21

Thus, the value of the expression 3a + b^2 - c is 21 when a = 2, b = 4, and c = 1.

Order of Operations (PEMDAS/BODMAS)

To avoid errors, always adhere to the order of operations:

  • Parentheses / Brackets
  • Exponents / Orders
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

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