Evaluate variable expressions involving integers

Learning Objectives Substitute given integer values for variables in single and multi-variable algebraic expressions. Apply the correct order of operations (PEMDAS/BODMAS) to evaluate expressions involving integers. Correctly compute operations with negative integers, including multiplication, division, and exponents. Evaluate polynomial expressions (e.g., linear, quadratic) for specific integer inputs. Differentiate between evaluating expressions like `(-x)^2` and `-x^2`. Analyze and solve multi-step problems by accurately evaluating variable expressions. Ever seen a weather forecast predict a temperature drop from 5° to -15° and wondered how they calculate the wind chill? 🥶 That calculation uses the exact skills you're about to learn! This tutorial will teach you ho...

TermDefinitionExample VariableA symbol, typically a letter like x or y, that represents a number. In this context, it will represent an integer.In the expression `7a - 4`, the variable is `a`. IntegerA whole number that can be positive, negative, or zero. Integers do not have fractional or decimal parts.`..., -5, -4, -3, -2, -1, 0, 1, 2, 3, ...` Algebraic ExpressionA mathematical phrase built from integers, variables, and operations (addition, subtraction, multiplication, division, exponents).`3x^2 - 2y + 5` is an algebraic expression. EvaluateTo find the single numerical value of an expression after substituting the given numbers for the variables.To evaluate `x + 10` when `x = -3`, you calculate `-3 + 10`, which equals `7`. SubstitutionThe action of replacing a variable with its assigne...

The Substitution Principle If `a = b`, then `a` can be replaced by `b` in any expression. This is the fundamental action of evaluation. To avoid common errors, always use parentheses when you substitute a value for a variable, especially if the value is negative. For example, to evaluate `x^2` for `x = -5`, write `(-5)^2`. Order of Operations (PEMDAS) 1. Parentheses (and other grouping symbols) 2. Exponents 3. Multiplication and Division (from left to right) 4. Addition and Subtraction (from left to right) This is the universal rule for the sequence of calculations. Following this order ensures that everyone who evaluates an expression will arrive at the same, correct answer. Integer Sign Rules for Multiplication/Division (+) \cdot (+) = (+), \quad (-) \cdot (-) = (...