How to Solve Equations with the Distributive Property like a Pro

Get the free Equations with the Distributive Property worksheet and other resources for teaching & understanding solving Equations with the Distributive Property

How to Solve Equations with the Distributive Property

Solving Equations with the Distributive Property happens when a linear equation has a term being distributed to multiple terms inside of a set of parenthesis. The first thing you must do is simplify by using the Distributive Property. You simplify using the Distributive Property by distributing the term in front of the parenthesis by multiplying it by everything on the inside of the parenthesis. After you use the Distributive Property, you solve the equations just like any other Two Step Equation. The first step in solving Two Step Equations is to get all of the constants (numbers) on one side of the equal sign, and the coefficient with the variable on the other side. In order to do this you must use the addition and subtraction property of equality to get the constants on the opposite side as the variable. Once the constants are separated from the variable, you must use the multiplication or division property of equality to cancel out the coefficient on the variable. You can always check your answer by substituting your solution back in to the equation for the variable.

Common Core Standard: 8.EE.C.7

Basic Topics: Combining Like Terms, Distributive Property, Two Step Equations, One Step Inequalities, Two Step Inequalities, Multi Step Inequalities

Return To: Home, 8th Grade

More Examples of Multi Step Equations with Distributive Property

So what is the distributive property anyway? Solving Equations with Distributive Property happens when a linear equation contains the distributive property. You can tell if the linear equation contains the distributive property if there is a term that is being distributed to multiple terms inside a set of parenthesis. You must first distribute according to the distributive property. Then you can solve the equation for the variable just like you would any two step equation.

4 Easy Steps for Solving Distributive Property Equations

Steps for solving the Equation with the Distributive Property above:

Distribute the two to the x and one inside the parenthesis.
Multiply the two times x and the two times one.
Add two to both sides.
Divide both sides by two to get the solution of x equals three.

Equations with Distributive Property Practice Problems Quiz

Video on the Free Distributive Property Equations Worksheet

Watch our free video on how to solve 2 step equations with Distributive Property. This video shows how to solve problems that are on our free solving Equations with Distributive Property worksheet that you can get by submitting your email above.

Watch the free Equations with the Distributive Property video on YouTube here: Equations with the Distributive Property

Video Transcript:

This video we’re going to show you some problems from our equations with the two step equations with distributive property worksheet. This video is about learning how to solve two step equations with distributive property. Our first problem on our equations with the distributive property worksheet is 2 times the quantity X minus 1 equals 4. The first step or the first thing you have to do when you have the distributive property is you have to distribute whatever is on the outside of the parenthesis to everything on the inside of the parenthesis. In the case of this problem we have to take 2 times it by X. 2 times X minus and then 2 times 1 and then you bring down your equals 4.

We’ve taken what’s on the outside of the parenthesis which in this case is 2 and multiplied it or distribute it it to everything on the inside of the parenthesis. After you do that you have 2 times X minus 2 times 1 equals 4. Of course 2 times X is 2x and then 2 times 1 is 2. Now our equation is 2x minus 2 equals 4. Now we have to get the variable on one side by itself and constants on the other in order to do that we’re going to add 2 to both sides. That the twos will cancel and then you have 2x on this side of the equation and then 4 plus 2 which is 6. On this side of the equation then the last step is to divide both sides by 2 because the coefficient on 2x is 2 and this is like saying 2 times X the opposite of 2 times X is 2 divided by 2. Now we have X on this side and then 6 divided by 2 on this side which is 3 and that’s our solution. This is a short explanation what is distributive property example.

The second problem on our equations with distributive property worksheet gives us five times the quantity 5x minus 5 equals 50. Once again the first step is to distribute everything on the outside to everything on the inside of the parenthesis. We will do 5 times 5x minus you keep the sign in the middle the same five times five, then you bring down your equals and then you bring down your constant on this side which is 50. Then to simplify you do five times 5x which is 25 X minus five times 5 which is 25 equals 50. Now we have to solve for X. In order to do that we’re going to add 25 here because we have to get rid of all the constants on the same side as . These 25s cancel you bring down your 25 X and then you do 50 plus 25 over here which is 75. Then the last step is to divide by 25 because we have to cancel the coefficient on the X. These guys cancel you’re left with just X on this side and then 75 divided by 25 is 3. The solution to number 2 is x equals 3.

The last problem we’re going to go over on our worksheet for the equations with a distributive property is number 3. Number 3 gives us 20 equals negative 10 times the quantity X plus 8. Once again the first step is to distribute the negative 10 or whatever’s on the outside to everything on the inside and this time you need to be careful because this is a negative 10. You have to distribute a negative 10. You have to include the negative when you distribute. This is like negative 10 times X plus and then negative 10, will write it in parenthesis because it’s negative times 8. Now we have 20 equals negative 10 times X plus negative 10 times 8. When we simplify this negative 10 times X is negative 10 X and then negative 10 times 80 is negative 80. You bring down your equal sign and your constant on the other side. Now we have to get rid of this negative 80 and in order to do that we’re gonna go ahead and add 80 to both sides. This negative 80 and this positive 80 will cancel and then you bring down your negative 10 X and then 20 plus 80 is 100. The final step is to get X by itself. In order to do that we divide both sides by negative 10. These guys will cancel and your have X on this side and then 100 divided by negative 10 is negative 10.

That will do it for our 2 step equations with distributive property worksheet.