Lesson 5: Evaluate Algebraic Expressions

Property

An algebraic expression is a collection of constants and variables joined by algebraic operations.
To evaluate an algebraic expression, replace each variable in the expression with its given value, then simplify the resulting expression using the order of operations.

Examples

• Evaluate $4y - 9$ for $y = 5$: Substitute $5$ for $y$ to get $4(5) - 9 = 20 - 9 = 11$.
• Evaluate $\frac{x+7}{x-2}$ for $x=5$: Substitute $5$ for $x$ to get $\frac{5+7}{5-2} = \frac{12}{3} = 4$.
• Evaluate $a^2 + 2b^2$ for $a = 4$ and $b = 3$: Substitute the values to get $4^2 + 2(3^2) = 16 + 2(9) = 16 + 18 = 34$.

Explanation

Evaluating an expression is like using a recipe. The expression is the formula, the variables are the ingredients, and the given values are the specific amounts you must plug in to find the final result.

Property

To evaluate an algebraic expression with decimals, substitute the given value for the variable and simplify the expression using the order of operations.

Examples

• Evaluate $4.5x - 2.1$ for $x = 3$.

• Evaluate $\frac{z}{0.5} + 7.8$ for $z = 4.3$.