Solve linear equations

Learning Objectives Solve multi-step linear equations with variables on both sides. Solve linear equations containing complex fractions and decimals by clearing the denominators or decimal places. Rearrange literal equations to solve for a specified variable. Identify whether a linear equation has one solution, no solution (contradiction), or infinitely many solutions (identity). Apply the properties of equality and the distributive property with 100% accuracy in complex algebraic manipulations. Set up and solve linear equations from word problems involving rates, mixtures, or geometric formulas. Ever wondered how engineers calculate the precise amount of force needed for a satellite's thrusters or how financial analysts model investment growth? 🛰️ It all starts with ma...

TermDefinitionExample Linear Equation in One VariableAn equation that can be written in the standard form ax + b = c, where a, b, and c are real numbers and a ≠ 0. Its graph is a horizontal line, and it has at most one solution.3(x - 2) + 5 = 14 is a linear equation because it can be simplified to 3x - 1 = 14, which fits the form ax + b = c. Literal EquationAn equation that consists of several variables (letters), often representing a formula. The goal is to solve for one variable in terms of the others.The formula for the perimeter of a rectangle, P = 2l + 2w, is a literal equation. You could solve for w to get w = (P - 2l) / 2. IdentityAn equation that is true for all possible values of the variable. When solving, the variables will cancel out, leaving a true statement.2(x + 3) = 2x + 6...

Addition Property of Equality If a = b, then a + c = b + c Use this rule to isolate the variable term. If a term is being added to your variable term, subtract it from both sides of the equation, and vice versa. Multiplication Property of Equality If a = b and c ≠ 0, then ac = bc Use this rule to solve for the variable once it has been isolated. If the variable is multiplied by a coefficient, divide both sides by that coefficient. Distributive Property a(b + c) = ab + ac Use this rule to eliminate parentheses from an equation. Multiply the term outside the parentheses by every term inside the parentheses.