Distributive Property Equations Worksheet, Examples, and Formula

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

4 EASY Steps for Solving Equations with the Distributive Property

Key Points about Distributive Property Equations

  • The distributive property is a fundamental concept in mathematics that is used to simplify expressions and solve equations.
  • The distributive property is an essential tool for solving equations in algebra and is widely used in geometry.
  • By using the distributive property, mathematicians can solve complex equations quickly and efficiently.

How to Solve Using 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.

The distributive property is a fundamental concept in mathematics that is used to simplify expressions and solve equations. It is a powerful tool that allows mathematicians to multiply a single term by a sum or difference of terms. This property is widely used in algebra, where it is used to solve equations that contain variables.

The distributive property is an essential tool for solving equations in algebra. It allows mathematicians to simplify expressions and solve equations by breaking them down into smaller, more manageable parts. By using this property, mathematicians can solve complex equations quickly and efficiently. The distributive property is also used in geometry, where it is used to simplify expressions involving areas and volumes.

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
Related Topics: Two Step Equations, Multi Step Equation, Equations with Variables on Both Sides
Return To: Home, 8th Grade

Equations with the Distributive Property

What are Distributive Properties in Math?

The distributive property is a fundamental concept in mathematics that explains how to simplify expressions that involve multiplication and addition. It is also known as the distributive law of multiplication and division. Essentially, it states that when you multiply a number by a sum, you can distribute the multiplication across each term in the sum.

For example, consider the expression 2 x (3 + 4). We can apply the distributive property to simplify this expression as follows:

2 x (3 + 4) = 2 x 3 + 2 x 4 = 6 + 8 = 14

Here, we distributed the multiplication of 2 across the terms 3 and 4, and then added the results. This is a simple example, but the distributive property can be applied to much more complex expressions as well.

The distributive property is particularly useful when dealing with algebraic expressions that involve variables. For example, consider the expression 3(x + 2). We can apply the distributive property to simplify this expression as follows:

3(x + 2) = 3x + 3(2) = 3x + 6

Here, we distributed the multiplication of 3 across the terms x and 2, and then added the results. This gives us a simplified expression that is easier to work with.

In general, the distributive property applies to any expression of the form a(b + c), where a, b, and c are numbers or variables. By distributing the multiplication across the sum, we can simplify the expression and make it easier to work with.

It is important to note that the distributive property only applies to addition within parentheses. If the expression involves subtraction within parentheses, the distributive property does not apply. In such cases, we need to use a different method to simplify the expression.

 

Solving Distributive Property Equations

When solving distributive property equations, the goal is to isolate the variable on one side of the equation. This is done by using inverse operations to undo any operations that are being performed on the variable. The distributive property is a useful tool in solving equations because it allows us to simplify expressions before isolating the variable.

To solve an equation using the distributive property, first distribute the number outside the parentheses to each term inside the parentheses. Then, combine like terms and simplify the expression. Next, use inverse operations to isolate the variable on one side of the equation. Finally, check the solution by plugging it back into the original equation.

Here is an example of solving an equation using the distributive property:

3(x + 4) = 21

First, distribute the 3 to each term inside the parentheses:

3x + 12 = 21

Next, subtract 12 from both sides to isolate the variable:

3x = 9

Finally, divide both sides by 3 to solve for x:

x = 3

The solution to the equation is x = 3.

It is important to note that the distributive property can also be used in reverse to factor expressions. This can be helpful in simplifying expressions before solving equations. For example, the expression 3x + 9 can be factored as 3(x + 3).

In summary, the distributive property is a powerful tool in solving equations and simplifying expressions. By distributing a number to each term inside parentheses, we can simplify expressions before isolating the variable. This allows us to solve equations more efficiently and accurately.

Equations with the Distributive Property Solution

3 Simple Distributive Property Equation Examples

The distributive property is a fundamental concept in algebra that states that the product of a number and the sum or difference of two other numbers is equal to the sum or difference of the products of the number and each of the other two numbers. In other words, the distributive property allows us to multiply a single term by two or more terms inside a set of parentheses.

Steps for solving the Equation with the Distributive Property above:

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

Distributive Property with Addition and Subtraction

One common application of the distributive property is to simplify expressions that involve addition or subtraction. For example, consider the following equation:

3(x + 4) - 2(x - 1) = 11

To solve this equation, we can use the distributive property to expand the parentheses and simplify the resulting expression:

3x + 12 - 2x + 2 = 11

Next, we can combine like terms and solve for x:

x + 14 = 11
x = -3

Distributive Property and Fractions

The distributive property can also be used to simplify expressions that involve fractions. For example, consider the following equation:

2/3(x + 6) = 4

To solve this equation, we can use the distributive property to eliminate the fraction:

2/3x + 4 = 4

Next, we can subtract 4 from both sides and multiply by the reciprocal of 2/3 to solve for x:

2/3x = 0
x = 0

Distributive Property and Order of Operations

The distributive property is also useful for simplifying expressions that involve multiple operations. For example, consider the following equation:

4 + 2(3x - 1) = 10

To solve this equation, we can use the distributive property to simplify the expression inside the parentheses:

4 + 6x - 2 = 10

Next, we can combine like terms and solve for x:

6x + 2 = 10
6x = 8
x = 4/3

In summary, the distributive property is a powerful tool for simplifying algebraic expressions and solving equations. By applying the distributive property correctly, we can eliminate parentheses, combine like terms, and isolate variables to find their values.

 

5 Quick Equations with Distributive Property Practice Problems

/5

Equations with the Distributive Property Quiz

Click Start to begin the practice quiz!

1 / 5

Solve the equation for x.

5(5x - 5) = 50

2 / 5

Solve the equation for x.

12(x - 5) = 60

3 / 5

Solve the equation for x.

-2(2x + 9) = 2

4 / 5

Solve the equation for x.

2(x - 1) = 4

5 / 5

Solve the equation for x.

20 = -10(x + 8)

Your score is

0%

 

Solving Equations with Distributive Property

When solving algebraic equations, the distributive property is a useful tool that can simplify the equation and make it easier to solve. The distributive property states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the products. This property can be used to solve equations that involve variables and expressions with multiple terms.

To solve an equation with the distributive property, the first step is to distribute the coefficient or constant to each term in the parenthesis. This can be done by multiplying the coefficient or constant by each term in the parenthesis. Once this is done, the equation can be simplified by combining like terms and isolating the variable on one side of the equation.

For example, consider the equation 3(x + 2) = 15. To solve this equation, the distributive property can be used to distribute the coefficient 3 to each term in the parenthesis, resulting in 3x + 6 = 15. Next, the equation can be simplified by subtracting 6 from both sides, resulting in 3x = 9. Finally, the variable can be isolated by dividing both sides by 3, resulting in x = 3.

It is important to note that the distributive property can also be used to simplify algebraic expressions with multiple terms. To simplify an expression with the distributive property, the first step is to distribute the coefficient or constant to each term in the expression. Once this is done, the expression can be simplified by combining like terms.

In summary, the distributive property is a powerful tool that can be used to simplify algebraic equations and expressions. By distributing the coefficient or constant to each term in the parenthesis, equations can be simplified and variables can be isolated. With practice, solving equations with the distributive property can become second nature to students learning algebra.

 

Distributive Property Steps

When solving equations using the distributive property, there are a few steps that need to be followed. These steps are essential to ensure that the equation is solved correctly.

The steps for solving equations using the distributive property are as follows:

  1. Distribute the number outside the parentheses to each term inside the parentheses. This means that you multiply the number outside the parentheses by each term inside the parentheses. For example, if you have the equation 3(x+2), you would distribute the 3 to both x and 2, resulting in 3x+6.

  2. Combine like terms. This means that you add or subtract terms that have the same variable and exponent. For example, if you have the equation 2x+3x, you would combine the x terms to get 5x.

  3. Move all the variable terms to one side of the equation and all the constant terms to the other side. This means that you want to isolate the variable on one side of the equation. For example, if you have the equation 5x+2=17, you would subtract 2 from both sides to get 5x=15.

  4. Solve for the variable. This means that you want to find the value of the variable that makes the equation true. For example, if you have the equation 5x=15, you would divide both sides by 5 to get x=3.

It is important to practice solving equations using the distributive property to become proficient in these steps. By practicing, you will become more confident in your ability to solve these types of equations.

 

Solve Using Distributive Property FAQ

How can you use the distributive property to simplify equations?

The distributive property is a powerful tool for simplifying equations. It allows you to distribute a number or variable to every term inside a set of parentheses. For example, if you have the equation 2(x + 3), you can use the distributive property to simplify it to 2x + 6. This is because you distribute the 2 to both x and 3.

What are some common mistakes to avoid when using the distributive property to solve equations?

One common mistake when using the distributive property is forgetting to distribute the number or variable to every term inside the parentheses. Another mistake is not combining like terms after distributing. It’s important to remember to simplify the equation as much as possible before solving for the variable.

What are some examples of equations that can be solved using the distributive property?

Equations that involve multiplication and addition or subtraction can often be solved using the distributive property. For example, 3(x + 2) = 15 can be solved by distributing the 3 to both x and 2, resulting in 3x + 6 = 15.

What is the difference between solving equations with the distributive property on one side versus both sides?

Solving equations with the distributive property on one side means that you only distribute the number or variable to one side of the equation. For example, 2(x + 3) = 10 can be solved by distributing the 2 to only the left side of the equation, resulting in 2x + 6 = 10. Solving equations with the distributive property on both sides means that you distribute the number or variable to both sides of the equation. For example, 2(x + 3) + 4 = 10 + 2(x - 1) can be solved by distributing the 2 to both sides of the equation, resulting in 2x + 10 = 2x + 0.

What are some strategies for teaching the distributive property to students?

One strategy for teaching the distributive property is to use visual aids, such as manipulatives or diagrams, to help students understand the concept. Another strategy is to provide real-world examples of how the distributive property is used, such as in calculating prices at a store.

How can you check your work when using the distributive property to solve equations?

One way to check your work is to substitute your solution back into the original equation and see if it makes the equation true. Another way is to simplify the equation as much as possible and make sure that both sides are equal.

How do you use distributive property in two step equations?

To use the distributive property in two-step equations, you first simplify any expressions inside parentheses by distributing any coefficients. Then, you use inverse operations to isolate the variable on one side of the equation. For example, 3(x + 2) - 4 = 13 can be solved by distributing the 3 to both x and 2, resulting in 3x + 6 - 4 = 13. Then, you simplify the equation to 3x + 2 = 13, and isolate the variable by subtracting 2 from both sides, resulting in 3x = 11. Finally, you solve for x by dividing both sides by 3, resulting in x = 11/3.

 

Distributive Property Equations Worksheet Video Explanation

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.

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Free Equations with the Distributive Property Worksheet

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