Solving Equations with the Distributive Property
Solving Equations with the Distributive Property walks Grade 6 students through the complete process for solving multi-step linear equations: use the distributive law to expand parentheses, combine like terms, then isolate the variable using inverse operations. This systematic method is covered in Yoshiwara Elementary Algebra Chapter 4: Applications of Linear Equations and is essential for solving equations where the variable appears inside parentheses or with coefficients on multiple sides.
Key Concepts
Property Steps for Solving Linear Equations. 1. Use the distributive law to remove any parentheses. 2. Combine like terms on each side of the equation. 3. By adding or subtracting the same quantity on both sides of the equation, get all the variable terms on one side and all the constant terms on the other. 4. Divide both sides by the coefficient of the variable to obtain an equation of the form $x = a$.
Examples Solve $3(x 4) = 9$. First, distribute the 3 to get $3x 12 = 9$. Add 12 to both sides to get $3x = 21$. Finally, divide by 3 to find $x = 7$. Solve $5(y+1) = 2y 4$. Distribute to get $5y+5 = 2y 4$. Subtract $2y$ from both sides, then subtract 5 from both sides to get $3y = 9$. Divide by 3 to find $y= 3$. Solve $25 4x = 2x 5(2 x)$. Distribute to get $25 4x = 2x 10 + 5x$. Combine like terms to get $25 4x = 7x 10$. Add $4x$ to both sides, then add 10 to both sides to get $35 = 11x$, so $x = \frac{35}{11}$.
Explanation When an equation has parentheses, first use the distributive law to clear them. After that, tidy up by combining like terms on each side. This simplifies the equation, making it easier to isolate the variable and find your solution.
Common Questions
How do you solve an equation with the distributive property?
First, apply the distributive law to remove parentheses (multiply the factor through). Then combine like terms on each side, and finally isolate the variable using addition, subtraction, multiplication, or division.
What is the distributive property?
The distributive property says a(b + c) = ab + ac. It expands a product involving a sum or difference into individual terms.
What order do you follow when solving linear equations?
Use distributive property first, then combine like terms on each side, then move variable terms to one side, then solve for the variable.
Where is solving with the distributive property in Yoshiwara Elementary Algebra?
This topic is in Chapter 4: Applications of Linear Equations of Yoshiwara Elementary Algebra.
What is a common mistake when applying the distributive property?
Forgetting to multiply the factor by every term inside the parentheses. For example, 2(x + 3) = 2x + 6, not 2x + 3.