Evaluate one variable expressions

Learning Objectives Define and identify variables, constants, and terms in an algebraic expression. Accurately substitute numerical values for variables in an expression. Apply the order of operations (PEMDAS/BODMAS) correctly to simplify expressions. Evaluate one-variable expressions involving integers, fractions, and exponents. Identify and avoid common errors when evaluating expressions, particularly with negative numbers. Solve real-world problems by evaluating one-variable expressions. Ever wonder how engineers calculate the stress on a bridge 🌉 or how much interest your savings account will earn? It all starts with understanding how to use formulas! In this lesson, you'll learn the fundamental skill of evaluating one-variable expressions. This means taking an ex...

TermDefinitionExample VariableA symbol, usually a letter (like x, y, or a), that represents an unknown or changing numerical value.In the expression `2x + 5`, 'x' is the variable. Algebraic ExpressionA mathematical phrase that contains numbers, variables, and operation symbols (like +, -, ×, ÷), but no equality sign.`3y - 7` or `x^2 + 2x - 1` are algebraic expressions. ConstantA value that does not change; it is a fixed number in an expression.In the expression `2x + 5`, '5' is the constant. CoefficientThe numerical factor that multiplies a variable in a term.In the term `3x`, '3' is the coefficient. In `y`, the coefficient is `1`. SubstituteTo replace a variable in an expression with a specific numerical value.If `x = 4`, we substitute `4` for `x` in `2x + 5...

Order of Operations (PEMDAS/BODMAS) 1. Parentheses/Brackets 2. Exponents/Orders 3. Multiplication and Division (from left to right) 4. Addition and Subtraction (from left to right) This rule must be followed precisely to ensure you arrive at the correct numerical value for any expression. Operations within parentheses are always performed first, followed by exponents, then multiplication and division (whichever comes first from left to right), and finally addition and subtraction (whichever comes first from left to right). Substitution Principle Replace each occurrence of the variable with its given numerical value. Before performing any calculations, every instance of the variable in the expression must be replaced by the number it represents. It's good practice to use...