Solve advanced linear equations

Learning Objectives Apply the distributive property to simplify linear equations. Combine like terms on one or both sides of a linear equation. Solve linear equations with variables on both sides of the equals sign. Solve multi-step linear equations involving fractions or decimals. Identify and correct common errors when solving advanced linear equations. Check their solutions to verify accuracy in advanced linear equations. Ever wonder how engineers calculate the exact dimensions for a bridge, or how much time it takes to save up for a new gadget? 🌉💰 Advanced linear equations are the secret sauce! In this lesson, you'll dive deeper into solving linear equations, tackling problems that require more steps and careful organization. You'll learn powerful techniques...

TermDefinitionExample Linear EquationAn equation that can be written in the form Ax + B = C, where x is the variable, and A, B, and C are constants. When graphed, it forms a straight line.3x + 7 = 16 Distributive PropertyA property that allows you to multiply a sum by multiplying each addend separately and then adding the products. It's essential for removing parentheses in equations.2(x + 3) = 2x + 6 Like TermsTerms that have the same variable raised to the same power. Only like terms can be combined through addition or subtraction.In 5x + 2x - 7, '5x' and '2x' are like terms, combining to '7x'. CoefficientThe numerical factor of a term that contains a variable. It tells you how many of the variable you have.In the term 7x, 7 is the coefficient. Constan...

Distributive Property $$a(b + c) = ab + ac$$ Use this rule to eliminate parentheses by multiplying the term outside the parentheses by each term inside. Remember to distribute to ALL terms inside. Properties of Equality If a = b, then: 1. $a + c = b + c$ (Addition Property) 2. $a - c = b - c$ (Subtraction Property) 3. $ac = bc$ (Multiplication Property) 4. $a/c = b/c$ (Division Property, where $c \neq 0$) These properties state that whatever operation you perform on one side of an equation, you must perform the exact same operation on the other side to maintain equality. This is how you move terms and isolate the variable. Combining Like Terms $$Ax + Bx = (A+B)x$$ Before isolating the variable, simplify each side of the equation by combining terms that have t...