Substitute a number in for a variable and simplify
Evaluate Algebraic Expressions
Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression given the value of each variable in the expression.
How to: Evaluate Algebraic Expressions
Identify Variables and Values: Look at the problem to determine which variables are present and what values they have been assigned.
Replace Variables with Values: Substitute each variable in the expression with the given value. Be sure to maintain any coefficients or operators attached to the variables.
Follow the Order of Operations: After substitution, simplify the expression by following the order of operations, also known by the acronym PEMDAS:
Parentheses: Start by simplifying expressions within parentheses or other grouping symbols.
Exponents: Next, calculate the powers or exponents.
Multiplication and Division: Then perform all multiplication and division from left to right.
Addition and Subtraction: Finally, complete any addition and subtraction from left to right.
Combine Like Terms: If the expression has like terms (terms with the same variable and exponent), combine them by adding or subtracting the coefficients.
In the next example we show how to substitute various types of numbers into a mathematical expression.
Evaluate [latex]x+7[/latex] when:
[latex]x=3[/latex]
[latex]x=12[/latex]
1. To evaluate, substitute [latex]3[/latex] for [latex]x[/latex] in the expression, and then simplify.
[latex]x+7[/latex]
Substitute.
[latex]\color{red}{3}\color{black}+7[/latex]
Add.
[latex]10[/latex]
When [latex]x=3[/latex], the expression [latex]x+7[/latex] has a value of [latex]10[/latex].
2. To evaluate, substitute [latex]12[/latex] for [latex]x[/latex] in the expression, and then simplify.
[latex]x+7[/latex]
Substitute.
[latex]\color{red}{12}\color{black}+7[/latex]
Add.
[latex]19[/latex]
When [latex]x=12[/latex], the expression [latex]x+7[/latex] has a value of [latex]19[/latex].
Notice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.
Evaluate the expression [latex]2x + 7[/latex] for each value for [latex]x[/latex].