Evaluate variable expressions

Learning Objectives Define key terms such as variable, expression, and evaluate. Substitute given numerical values for variables in algebraic expressions. Correctly apply the order of operations when evaluating expressions. Evaluate one-variable expressions involving addition, subtraction, multiplication, and division. Evaluate multi-variable expressions with given numerical values. Identify and correct common errors made when evaluating expressions. Have you ever seen a recipe that says 'add 'x' cups of flour' and then tells you 'x = 2'? 🤔 That's a bit like what we're doing today! In this lesson, you'll learn how to find the numerical value of an algebraic expression when you know what the letters (variables) stand for. This sk...

TermDefinitionExample VariableA letter or symbol that represents an unknown or changing numerical value.In the expression `x + 5`, 'x' is the variable. Algebraic ExpressionA mathematical phrase that contains variables, numbers, and at least one operation symbol (like +, -, ×, ÷). It does not have an equals sign.`3y - 7` is an algebraic expression. ConstantA number in an expression whose value does not change.In the expression `x + 5`, '5' is the constant. TermParts of an expression that are separated by addition or subtraction signs.In the expression `3y - 7`, `3y` and `7` are the terms. SubstitutionThe process of replacing a variable with a specific numerical value.If `x = 2`, substituting `2` for `x` in `x + 5` gives `2 + 5`. EvaluateTo find the numerical value of an...

Substitution Principle Replace each variable in the expression with its given numerical value. When you are given the value of a variable, you must carefully substitute that number in place of every instance of that variable in the expression. Remember that a number next to a variable (like `3x`) means multiplication (`3 \times x`). Order of Operations (PEMDAS/BODMAS) $$ \text{P} \text{arentheses} \text{ (or B} \text{rackets)} \\ \text{E} \text{xponents} \text{ (or O} \text{rders)} \\ \text{M} \text{ultiplication and D} \text{ivision (from left to right)} \\ \text{A} \text{ddition and S} \text{ubtraction (from left to right)} $$ After substituting the values, follow this specific order to perform the calculations. Always work from left to right for multiplication/division an...