Evaluate multi-variable expressions

Learning Objectives Define what a variable and a multi-variable expression are. Substitute given numerical values for variables in an expression. Apply the order of operations (PEMDAS/BODMAS) correctly when evaluating expressions. Evaluate multi-variable expressions involving positive and negative integers. Simplify expressions to a single numerical value after substitution. Identify the different parts of an algebraic expression (terms, coefficients, variables, constants). Ever wonder how scientists predict weather or how game developers calculate scores? 🤔 It all starts with understanding how to use formulas with different numbers! In this lesson, you'll learn how to 'evaluate' expressions that have more than one letter, called variables. This skill is sup...

TermDefinitionExample VariableA letter or symbol (like x, y, or a) that represents an unknown or changing numerical value.In the expression $x + 5$, 'x' is the variable. ExpressionA mathematical phrase that contains numbers, variables, and operation symbols (like +, -, ×, ÷) but does not have an equality sign.$3a + 2b - 7$ Multi-variable ExpressionAn algebraic expression that contains two or more different variables.$5x - 2y + z$ EvaluateTo find the numerical value of an expression by substituting given numbers for the variables and then performing the indicated operations.To evaluate $x+y$ if $x=2$ and $y=3$, you get $2+3=5$. SubstitutionThe process of replacing a variable in an expression with its given numerical value.If $a=4$, substituting into $2a$ gives $2(4)$. ConstantA n...

Substitution Rule Replace each variable in the expression with its given numerical value. This is the first step in evaluating any expression. Always use parentheses around the substituted value, especially for negative numbers or when a variable is multiplied by a coefficient, to prevent calculation errors. Order of Operations (PEMDAS/BODMAS) $P ext{(arentheses)} ightarrow E ext{(xponents)} ightarrow M ext{(ultiplication)} / D ext{(ivision)} ext{(from left to right)} ightarrow A ext{(ddition)} / S ext{(ubtraction)} ext{(from left to right)}$ After substituting the values, follow this specific order to perform all calculations. This ensures that everyone gets the same correct answer for any given expression.