Solve equations with variables on both sides

Learning Objectives Identify terms with variables and constants on both sides of an equation. Apply inverse operations to move variable terms to one side of an equation. Combine like terms to simplify equations. Isolate the variable using inverse operations to find the solution. Verify their solutions by substituting the value back into the original equation. Solve multi-step linear equations with variables on both sides. Ever wonder how two different cell phone plans, one with a monthly fee and another with a per-minute charge, could cost the same? 🤔 Equations with variables on both sides help us figure that out! In this lesson, you'll learn how to solve equations where the unknown quantity (variable) appears on both sides. This skill is crucial for solving more comp...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal, separated by an equals sign (=).$3x + 5 = 2x - 1$ VariableA symbol, usually a letter, that represents an unknown value.In $x + 7 = 10$, $x$ is the variable. ConstantA term that has a fixed value and does not contain a variable.In $3x + 5 = 2x - 1$, $5$ and $-1$ are constants. TermA single number, a variable, or numbers and variables multiplied together.In $3x + 5 = 2x - 1$, $3x$, $5$, $2x$, and $-1$ are all terms. Like TermsTerms that have the exact same variable raised to the same power. Constants are also like terms.$3x$ and $2x$ are like terms; $5$ and $-1$ are like terms. Inverse OperationsOperations that undo each other (e.g., addition and subtraction, multiplication and division).To undo add...

Addition Property of Equality If $a = b$, then $a + c = b + c$. If you add the same number or expression to both sides of an equation, the equation remains balanced. Use this to move constant terms or variable terms by adding their opposite to both sides. Subtraction Property of Equality If $a = b$, then $a - c = b - c$. If you subtract the same number or expression from both sides of an equation, the equation remains balanced. Use this to move constant terms or variable terms by subtracting them from both sides. Multiplication Property of Equality If $a = b$, then $ac = bc$ (where $c \neq 0$). If you multiply both sides of an equation by the same non-zero number, the equation remains balanced. Use this to eliminate division or to clear fractions in an equation....