Evaluate variable expressions with whole numbers

Learning Objectives Define key terms such as variable, expression, and evaluate. Correctly substitute whole number values for variables in algebraic expressions. Apply the order of operations (PEMDAS/BODMAS) to simplify numerical expressions resulting from substitution. Accurately calculate the numerical value of variable expressions given whole number assignments for variables. Identify and correct common errors made when evaluating variable expressions. Explain the importance of evaluating expressions in real-world problem-solving contexts. Ever wonder how engineers calculate the strength of a bridge or how game developers determine character scores? 🎮 It all starts with understanding how to evaluate expressions! In this lesson, you'll learn the fundamental skill of...

TermDefinitionExample VariableA symbol, usually a letter (like x, y, or a), that represents an unknown or changing numerical value.In the expression `3x + 5`, 'x' is the variable. Algebraic ExpressionA mathematical phrase that contains variables, numbers, and at least one operation (like addition, subtraction, multiplication, or division). It does not contain an equals sign.`2y - 7` or `x^2 + 3z` are algebraic expressions. Whole NumbersThe set of non-negative integers: {0, 1, 2, 3, ...}. These are the counting numbers plus zero.5, 12, 0, 100 are all whole numbers. EvaluateTo find the numerical value of an expression by substituting given values for the variables and performing the indicated operations.To evaluate `4x` when `x = 3` means to find `4 * 3`, which is 12. SubstituteTo...

Substitution Principle If a variable in an expression is assigned a specific numerical value, replace every instance of that variable with the given number. This is the first step in evaluating any variable expression. Always replace the variable with its assigned value before performing any calculations. For example, if you have `x^2` and `x=5`, you substitute to get `5^2`. Order of Operations (PEMDAS/BODMAS) The sequence for performing operations is: 1. **P**arentheses (or **B**rackets) 2. **E**xponents (or **O**rders/Indices) 3. **M**ultiplication and **D**ivision (from left to right) 4. **A**ddition and **S**ubtraction (from left to right) After substituting the values, you must follow this specific order to simplify the resulting numerical expression. Failing to do so...