Identify equivalent linear expressions

Learning Objectives Define what a linear expression is and identify its components (terms, coefficients, constants, variables). Apply the commutative and associative properties of addition to rearrange terms in an expression. Apply the distributive property to expand linear expressions. Combine like terms within a linear expression. Simplify linear expressions to their simplest form. Determine if two linear expressions are equivalent by simplifying them. Have you ever seen two different ways to write a math problem that actually mean the same thing? 🤔 Today, we'll learn how to spot these 'math twins'! In this lesson, you'll discover how to identify when two linear expressions, even if they look different, are actually equivalent. Understanding this help...

TermDefinitionExample ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols (like +, -, ×, ÷), but does not have an equals sign.$3x + 5$ Linear ExpressionAn algebraic expression where the highest power of the variable is 1. There are no variables multiplied by themselves (like $x^2$) or divided by variables.$2x - 7y + 10$ TermParts of an expression separated by addition or subtraction signs. A term can be a number, a variable, or a product of numbers and variables.In $4x + 7 - 2y$, the terms are $4x$, $7$, and $-2y$. CoefficientThe numerical factor multiplied by a variable in a term.In $5x$, the coefficient is $5$. In $-y$, the coefficient is $-1$. ConstantA term in an expression that does not contain a variable; its value never changes.In $2x + 9$, th...

Commutative Property of Addition $a + b = b + a$ You can change the order of numbers or terms when adding without changing the sum. This helps rearrange terms to group like terms together. Associative Property of Addition $(a + b) + c = a + (b + c)$ You can change the grouping of numbers or terms when adding without changing the sum. This helps rearrange terms to group like terms together. Distributive Property $a(b + c) = ab + ac$ To multiply a number by a sum or difference, multiply the number by each term inside the parentheses. This is crucial for expanding expressions. Combining Like Terms $ax + bx = (a+b)x$ To combine like terms, add or subtract their coefficients while keeping the variable part the same. This simplifies expressions.