Solving Equations with Grouping Symbols
Solve equations containing parentheses and grouping symbols in Grade 9 Algebra. Distribute first, then combine like terms before isolating the variable.
Key Concepts
Property When equations contain symbols of inclusion such as parentheses, use the Distributive Property to eliminate them first. Then combine like terms and apply inverse operations to solve.
Examples Solve $a + 4(2a + 3) = 39$. Distribute the 4: $a + 8a + 12 = 39$. Combine like terms: $9a + 12 = 39$. Solve: $9a = 27$, so $a = 3$. To solve $6(c 3) = 24$, first distribute the 6: $6c 18 = 24$. Then add 18 to both sides: $6c = 42$. The solution is $c = 7$. In $3(x + 5) + 2x = 35$, distribute the 3 to get $3x + 15 + 2x = 35$. Combine terms: $5x + 15 = 35$. Solve to find $x = 4$.
Explanation Parentheses in an equation are like a locked treasure chest! You have to 'distribute' the number outside to every item inside to unlock it. This unwraps the equation, letting you combine terms and solve for the hidden variable. Multiplying everything inside the parentheses is the key that opens up the problem.
Common Questions
How do you solve equations that contain grouping symbols like parentheses?
Apply the distributive property first to remove all parentheses. Then combine like terms on each side, use inverse operations to move variables to one side and constants to the other, and solve for the variable.
What is the order of steps for solving equations with multiple grouping symbols?
Work from the innermost grouping symbols outward. Distribute, combine like terms, then apply addition/subtraction and finally multiplication/division operations to isolate the variable.
What is a common error when distributing a negative sign with grouping symbols?
Failing to distribute a negative sign to every term inside the parentheses is the most frequent mistake. When you see -(a + b), the result is -a - b, not -a + b. Double-check every sign after distributing.