Evaluating Algebraic Expressions

An expression in which some or all of the terms contain variables is an algebraic expression. If the values of the variables are known, we can evaluate the expression.

Evaluating algebraic expressions means finding the numerical value of the expression by substituting specific values for the variables and then performing the indicated mathematical operations.

We can evaluate an algebraic expression for different values of the variable.
To evaluate 3x + 1 for x = −2, we substitute −2 in place of x
3(−2) + 1 = −6 + 1 = −5

The following diagram shows some examples of evaluating algebraic expressions. Scroll down the page for more examples and solutions for algebraic expressions.

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Basic Steps to Evaluate Expressions

1. Identify the variable(s) in the expression.
   
2. Substitute each variable with its given value. It’s a good practice to put the substituted values in parentheses, especially when dealing with negative numbers or exponents. This helps avoid confusion with signs and operations.
   
3. Simplify using the order of operations (PEMDAS/BODMAS):
   Parentheses (or Brackets)
   Exponents (or Orders/Indices)
   Multiplication & Division (left to right)
   Addition & Subtraction (left to right)
   

Remember to use order of operations to evaluate and be careful with the minus signs.

Evaluating Algebraic Expressions
How to evaluate an algebraic expression when values are given for the variable(s)?

Examples:
Let x = -3, y = 7, z = -2
Evaluate x - 3y + 7

Let y = 2
Evaluate 9/y = 8y + 2

Let x = 3, y = -5
Evaluate 4x - 3y²

Let x = -2
Evaluate 3x³ - x² + 2x + 9

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How to Evaluate Expressions with Two Variables?

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Evaluating Algebraic Expressions

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How to Evaluate Expressions with One Variable?

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Basic Mathematics & Algebra : Substituting Values Into an Algebraic Expression
Substituting values into an algebraic expression in mathematics is easier to do if the numbers the values represent are given ahead of time.

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Examples:

1. Evaluate x + 3 for x = 7
   
2. Evaluate x² + x - 3 for x = 2
   
3. Evaluate y² + x³ + 7 for y = 2, x = 1
   
4. Evaluate 5 - x² for x = -2
   
5. Evaluate (3x)(5y) for x = -1, y = 2
   
6. Evaluate -7x² -5 + y² - x for x = -2, y = 4
   
7. Evaluate 3x² ÷ 12 + y for x = 4, y = -7
   

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