Evaluate variable expressions involving integers

Learning Objectives Substitute given integer values for variables in multi-term algebraic expressions. Apply the correct order of operations (PEMDAS/BODMAS) to evaluate complex expressions involving integers, exponents, and grouping symbols. Correctly evaluate expressions with exponents where the base is a negative integer. Manage sign rules accurately when performing multiple operations with positive and negative integers. Evaluate expressions containing absolute value functions with integer inputs. Deconstruct and solve problems by evaluating formulas from scientific or financial contexts. How does a financial model predict future profits based on different sales numbers, or a physics engine calculate the trajectory of an object? 🚀 It all boils down to plugging values int...

TermDefinitionExample VariableA symbol, usually a letter (like x, y, or a), that represents an unknown or changing numerical value.In the expression `5x - 3`, `x` is the variable. IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero...., -3, -2, -1, 0, 1, 2, 3, ... Algebraic ExpressionA mathematical phrase that can contain ordinary numbers, variables, and operators (like +, -, *, /). It does not contain an equals sign.`3a^2 - 2b + c` is an algebraic expression. EvaluateTo find the single numerical value of an expression after substituting given numbers for the variables.To evaluate `x + 5` when `x = -2`, you calculate `-2 + 5` to get `3`. SubstitutionThe process of replacing a variable in an expression with its given numerical value. It's crucial...

The Substitution Principle If `a = b`, then `a` may be replaced by `b` in any expression. This is the fundamental principle that allows us to evaluate expressions. When substituting a value for a variable, especially a negative integer, always enclose the value in parentheses to preserve the original operations. For example, `x^2` with `x = -3` becomes `(-3)^2`, not `-3^2`. Order of Operations (PEMDAS) 1. P (Parentheses) \\ 2. E (Exponents) \\ 3. MD (Multiplication & Division) [L to R] \\ 4. AS (Addition & Subtraction) [L to R] This hierarchy dictates the sequence for simplifying any mathematical expression. Follow it strictly to avoid errors. Multiplication and Division have equal priority and are performed from left to right. The same applies to Addition and Subtra...