Solving Equations with the Distributive Property

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a multiplier across terms inside parentheses.

Front

How do you apply the Distributive Property to the expression 5(2x - 10)?

Back

You multiply 5 by each term inside the parentheses: 5 * 2x - 5 * 10 = 10x - 50.

Front

What is the first step to solve the equation 5(2x - 10) = 30?

Back

Apply the Distributive Property: 10x - 50 = 30.

Front

How do you isolate the variable x in the equation 10x - 50 = 30?

Back

Add 50 to both sides to get 10x = 80, then divide by 10 to find x = 8.

Front

What is the solution to the equation 6(2n + 5) = 66?

Back

First, distribute: 12n + 30 = 66. Then, subtract 30 from both sides to get 12n = 36, and divide by 12 to find n = 3.

Front

How do you solve the equation 4(5 - x) = 8?

Back

Distribute: 20 - 4x = 8. Then, subtract 20 from both sides to get -4x = -12, and divide by -4 to find x = 3.

Front

What is the solution to the equation 6(x + 3) = 48?

Back

Distribute: 6x + 18 = 48. Subtract 18 from both sides to get 6x = 30, then divide by 6 to find x = 5.

Front

How do you use the Distributive Property to solve 4(x + 2) = 16?

Back

Distribute: 4x + 8 = 16. Subtract 8 from both sides to get 4x = 8, then divide by 4 to find x = 2.

Front

What is the importance of the Distributive Property in solving equations?

Back

It allows you to simplify expressions and equations, making it easier to isolate variables and find solutions.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.