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 4(5 - x)?

Back

You multiply 4 by both 5 and -x, resulting in 20 - 4x.

Front

What is the first step to solve the equation 4(5 - x) = 8?

Back

Use the Distributive Property to expand the left side: 20 - 4x = 8.

Front

How do you isolate the variable x in the equation 20 - 4x = 8?

Back

Subtract 20 from both sides to get -4x = -12, then divide by -4 to find x = 3.

Front

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

Back

First, distribute: 6x + 18 = 48. Then, isolate x to find x = 5.

Front

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

Back

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

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.

Front

In the equation 9(x + 3) = 27, what is the first step to solve for x?

Back

Distribute to get 9x + 27 = 27, then subtract 27 from both sides to find 9x = 0.

Front

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

Back

Distribute to get 12n + 30 = 66, then subtract 30 from both sides to find 12n = 36, and divide by 12 to get n = 3.

Front

What is the importance of checking your solution after solving an equation?

Back

Checking your solution ensures that the value satisfies the original equation, confirming that the solution is correct.