Evaluate linear expressions

Learning Objectives Define and identify linear expressions, variables, constants, and coefficients. Substitute given numerical values for variables in linear expressions. Apply the order of operations correctly when evaluating expressions. Calculate the numerical value of linear expressions involving positive and negative integers. Solve real-world problems by evaluating linear expressions. Explain the steps involved in evaluating a linear expression. Ever wonder how mathematicians predict how much money you'll earn based on hours worked, or how much paint you need for a room? 💰 It all starts with understanding expressions! In this lesson, you'll learn how to 'evaluate' linear expressions, which means finding their numerical value when you know what the...

TermDefinitionExample ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols (like +, -, ×, ÷). It does not have an equals sign.3x + 5 Linear ExpressionAn algebraic expression where the highest power of any variable is 1. There are no variables multiplied together (like xy) or variables in the denominator.2y - 7, 4a + 3b - 1 VariableA letter or symbol (like x, y, a, b) that represents an unknown or changing numerical value.In 5x + 2, x is the variable. ConstantA fixed numerical value in an expression that does not change.In 5x + 2, 2 is the constant. CoefficientThe numerical factor that multiplies a variable in an algebraic term.In 5x + 2, 5 is the coefficient of x. EvaluateTo find the numerical value of an expression by substituting specific numbers fo...

Order of Operations (PEMDAS/BODMAS) Parenthses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This rule dictates the sequence in which mathematical operations must be performed to ensure a single, correct answer for any expression. It can be remembered by the acronym PEMDAS or BODMAS. Substitution Principle Replace each instance of a variable with its given numerical value. Use parentheses around the substituted value, especially for negative numbers, to avoid errors. This principle allows us to convert an algebraic expression into a purely numerical one, which can then be simplified using the order of operations. For example, if $x = -3$, then $2x$ becomes $2(-3)$.