Solve linear equations

Learning Objectives Isolate a variable in multi-step linear equations with integers, decimals, and fractions. Solve linear equations that include variables on both sides of the equal sign. Apply the distributive property to solve linear equations containing parentheses. Identify linear equations that have no solution or infinitely many solutions. Solve literal equations for a specified variable. Translate a real-world scenario into a linear equation and solve it. Ever tried to split a bill with friends, including tax and tip? 🍕 You're using algebra to solve for what each person owes, which is a linear equation! This tutorial will refresh your skills in solving various types of linear equations, a fundamental tool in algebra. Mastering this is crucial for building the...

TermDefinitionExample Linear EquationAn algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the first power.`4x - 7 = 5` is a linear equation. Its graph is a straight line. VariableA symbol, usually a letter, used to represent an unknown numerical value.In the equation `2y + 1 = 11`, `y` is the variable. CoefficientThe numerical factor of a term that contains a variable.In the term `-5a`, the coefficient is `-5`. Inverse OperationsOperations that 'undo' each other. Addition and subtraction are inverse operations; multiplication and division are inverse operations.To solve `x + 8 = 10`, you use the inverse of addition, which is subtraction. You subtract 8 from both sides. Like TermsTerms that have the exact same...

Addition/Subtraction Properties of Equality If `a = b`, then `a + c = b + c` and `a - c = b - c`. Use these properties to move terms across the equal sign. To eliminate a term, you add or subtract it from both sides of the equation to maintain balance. Multiplication/Division Properties of Equality If `a = b`, then `ac = bc` and `a/c = b/c` (for `c ≠ 0`). Use these properties to isolate the variable once all other terms have been moved. To eliminate a coefficient, you multiply or divide both sides by it.