Have you ever needed the distributive property to solve a problem? Well, Trevor has a dilemma. He is having difficulty figuring out this problem.
Do you know how to solve this equation? To figure it out, you will have to apply the distributive property. Take a look at this Concept and you will know how to solve this equation by the end of it.
You already know that some number properties can help you solve equations.
The distributive property may also help you solve some equations.
This property states that when a factor is multiplied by the sum of two numbers, we can multiply each of the two numbers by that factor and then add them.
Multiplication can also be distributed over subtraction.
Here are two situations that show the distributive property.
Let's see how the distributive property can help us solve some multi-step equations.
Apply the distributive property to the left side of the equation. Multiply each of the two numbers inside the parentheses by 5 and then add those products.
Let's look at another one.
Now we can distribute the two by multiplying it by both of the terms inside the parentheses. Notice that the second term has a subtraction sign in front of it. Remember to include that sign when we multiply.
Now let's go back to the dilemma at the beginning of the Concept.
This is the equation that needs to be solved.
First, we have to simplify the left side of the equation by getting rid of the parentheses. We do this by multiply both of the terms inside the parentheses by 7.
Next, we solve this two-step equation. Subtract 14 from both sides of the equation.
Now we can solve the one-step equation by dividing both sides of the equation by 7.
This is our final answer.
states that you can multiply a term outside of a set of parentheses with the terms inside the parentheses to simplify the set of parentheses.
Here is one for you to try on your own.
Khan Academy The Distributive Property
Directions: Use the distributive property to solve each equation.