Identify equivalent linear expressions

Learning Objectives Define and identify the components of a linear expression, including terms, coefficients, and constants. Apply the distributive, commutative, and associative properties to rewrite and simplify linear expressions. Combine like terms to simplify a linear expression into its most concise form. Determine if two linear expressions are equivalent by simplifying both expressions algebraically. Verify the equivalence of two linear expressions by substituting a given value for the variable. Create an equivalent expression by factoring a linear expression. Is getting a 20% discount on a shirt and then paying a $5 shipping fee the same as paying the $5 fee first and then getting 20% off the total? Let's explore the algebra behind it! 🛒 This tutorial will teac...

TermDefinitionExample Linear ExpressionAn algebraic expression in which the highest exponent of any variable is one. It can be represented as a line when graphed.The expression `5x - 9` is linear. The expression `5x^2 - 9` is not. TermA single part of an expression, separated by addition or subtraction signs. It can be a number, a variable, or a product of numbers and variables.In the expression `7y - 4z + 12`, the terms are `7y`, `-4z`, and `12`. CoefficientThe numerical factor that is multiplied by a variable in a term.In the term `-3p`, the coefficient is `-3`. Like TermsTerms that have the exact same variable(s) raised to the exact same power(s). Constants are also considered like terms.`2x` and `-5x` are like terms. `2x` and `2y` are not. ConstantA term that does not contain any vari...

Distributive Property a(b + c) = ab + ac Use this rule to multiply a single term by every term inside a set of parentheses. This is essential for expanding expressions. Commutative Property of Addition a + b = b + a This rule states that you can reorder terms being added without changing the final result. It's useful for grouping like terms together. Combining Like Terms ax + bx = (a + b)x To simplify an expression, you can add or subtract the coefficients of terms that have the identical variable part.