Review: Distributive Property + Equations

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum or difference.

Front

How do you simplify the expression -3(-10x - 5)?

Back

By applying the Distributive Property, the expression simplifies to 30x + 15.

Front

What is the first step to solve the equation 9(2x + 8) = 270?

Back

First, distribute 9 to both terms inside the parentheses: 18x + 72 = 270.

Front

How do you isolate the variable x in the equation 9(2x + 8) = 270?

Back

Subtract 72 from both sides to get 18x = 198, then divide by 18 to find x = 11.

Front

What is the solution to the equation 2(6k - 1) = -38?

Back

First, distribute 2 to get 12k - 2 = -38. Then add 2 to both sides to get 12k = -36, and divide by 12 to find k = -3.

Front

How do you solve the equation -(n - 8) = -2?

Back

Distribute the negative sign to get -n + 8 = -2. Then subtract 8 from both sides to find -n = -10, leading to n = 10.

Front

What is the first step in solving the equation -11 + 3(b + 5) = 7?

Back

Distribute 3 to both terms inside the parentheses: -11 + 3b + 15 = 7.

Front

How do you isolate b in the equation -11 + 3(b + 5) = 7?

Back

Combine like terms to get 3b + 4 = 7, then subtract 4 from both sides to find 3b = 3, leading to b = 1.

Front

What does it mean to combine like terms in an expression?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

What is the importance of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming its correctness.