Equations with Variables on Both Sides Worksheet, Practice, and Examples

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4 SIMPLE steps for Solving Equations with Variables on Both Sides (Avoid these common mistakes)

 

Key Points about Equations with Variables on Both Sides

  • Equations with variables on both sides are a fundamental concept in algebra used to solve for an unknown variable that appears on both sides of the equation.
  • Linear equations with variables on both sides can be solved using algebraic methods by isolating the variable on one side of the equation.
  • Equations with variables on both sides are commonly used in real-world situations and solving word problems, making it an essential skill for success in algebra and higher-level mathematics.

Multi Step Equations with Variables on Both Sides

When solving Equations with Variables on Both Sides, you must follow certain steps. The first thing you must do is get all the variables on one side of the equation. In order to do this, you must use the addition and subtraction property of equality to add or subtract the term with the variable so that they are on the same side. The next step when solving Equations with Variables on Both Sides, is to get the constants on the other side of the equal sign. You also add or subtract a constant so that your constant gets cancelled on the same side as the variable on the equal sign. The last step when solving Equations with Variables on Both Sides is to divide both sides of the equation by the coefficient of the variable so that it will cancel out.

Equations with variables on both sides are a fundamental concept in algebra. These equations are used to solve for an unknown variable that appears on both sides of the equation. Linear equations with variables on both sides are a specific type of equation that can be solved using algebraic methods.

To solve linear equations with variables on both sides, one must isolate the variable on one side of the equation. This can be done by using inverse operations, such as adding or subtracting the same value from both sides of the equation. Once the variable has been isolated, its value can be determined.

Equations with variables on both sides are commonly used in real-world situations, such as calculating distances, rates, and time. They can also be used to solve word problems that involve multiple variables. Understanding how to solve equations with variables on both sides is an essential skill for success in algebra and higher-level mathematics.

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 the Distributive Property
Return To: Home, 8th Grade

Solving Equations with Variables on Both Sides

Linear Equations with Variables on Both Sides

Linear equations with variables on both sides are equations that have variables on both sides of the equal sign. These types of equations can be challenging to solve because the variable is not isolated on one side of the equation.

Concept of Variables on Both Sides

In equations with variables on both sides, the variable appears on both sides of the equation. For example, in the equation 2x + 3 = x + 7, the variable x appears on both sides of the equation. To solve this type of equation, it is necessary to isolate the variable on one side of the equation.

Isolating the Variable

Isolating the variable means moving all the terms containing the variable to one side of the equation and all the constants to the other side. This process allows the variable to be solved for. It is important to isolate the variable because it helps to simplify the equation and makes it easier to solve.

To isolate the variable, it is necessary to use inverse operations to undo any operations that are being performed on the variable. For example, if the variable is being added to both sides of the equation, it can be isolated by subtracting the variable from both sides.

It is essential to keep the equation balanced by performing the same operation on both sides of the equation. For example, if 2 is added to one side of the equation, 2 must also be added to the other side of the equation to keep it balanced.

In conclusion, understanding how to solve linear equations with variables on both sides is an essential skill in algebra. By isolating the variable and keeping the equation balanced, it is possible to solve these types of equations.

 

How to Solve Equations with Variables on Both Sides

When solving equations with variables on both sides, there are a few steps that need to be followed. These steps include simplification, application of operations, isolation of variable, and checking the solution. By following these steps, one can solve equations with variables on both sides with ease.

Simplification

The first step in solving equations with variables on both sides is to simplify the equation. This involves combining like terms and canceling out terms that appear on both sides of the equation. By simplifying the equation, it becomes easier to isolate the variable and solve the equation.

Application of Operations

The next step is to apply operations to both sides of the equation in order to isolate the variable. The operations that can be applied include addition, subtraction, multiplication, and division. It is important to apply the same operation to both sides of the equation in order to maintain balance and equality.

Isolate the Variable

Once the equation has been simplified and operations have been applied, the next step is to isolate the variable. This involves getting all variable terms on one side of the equation and all constant terms on the other side of the equation. By doing this, the variable can be solved using inverse operations.

Checking the Solution

After the variable has been isolated and solved, it is important to check the solution by plugging it back into the original equation. This ensures that the solution is correct and that the equation has been solved properly.

In summary, solving equations with variables on both sides involves simplification, application of operations, isolation of variable, and checking the solution. By following these steps, one can solve linear equations with ease. It is important to remember to maintain balance and equality throughout the process and to check the solution to ensure its accuracy.

Solving Equations with Variables on Both Sides Solution

2 Simple Equations with Variables on Both Sides Examples

Equations with variables on both sides can be challenging to solve, but with practice, they can become easier. In this section, we will cover basic examples and advanced exercises to help you understand how to solve equations with variables on both sides.

Steps for Solving the Equations with Variables on Both Sides Example above:

  1. Add fifty three to both sides of the equation so that you get all constants on one side together.
  2. Subtract five x from both sides.
  3. Divide both sides of the equations by negative two to get your solution of negative thirty three.

Basic Examples

To solve equations with variables on both sides, the first step is to simplify both sides of the equation by combining like terms. Then, move all the variable terms to one side of the equation and all the constant terms to the other side of the equation. Finally, solve for the variable.

For example, consider the equation:

3x + 5 = 2x + 9

To solve this equation, first, simplify both sides by combining like terms:

x + 5 = 9

Then, move all the variable terms to one side and all the constant terms to the other side:

x = 4

Therefore, the solution to the equation is x = 4.

Another example is:

2y – 3 = 4y + 1

Simplify both sides of the equation:

-2y – 3 = 1

Move all the variable terms to one side and all the constant terms to the other side:

-2y = 4

Solve for y:

y = -2

Therefore, the solution to the equation is y = -2.

Advanced Exercises

Equations with variables on both sides can become more complex when decimals or fractions are involved. For example:

1.5x – 0.25 = 0.5x + 1.25

To solve this equation, first, simplify both sides by combining like terms:

1x – 0.25 = 1.25

Then, move all the variable terms to one side and all the constant terms to the other side:

1x = 1.5

Solve for x:

x = 1.5

Therefore, the solution to the equation is x = 1.5.

In addition, web filters and domains can affect the availability of resources for solving equations with variables on both sides. However, there are many online tools and exercises available to help students practice and improve their skills in solving equations with variables on both sides.

In summary, solving equations with variables on both sides requires simplifying both sides, moving all the variable terms to one side, and all the constant terms to the other side. With practice and patience, anyone can master this skill.

 

5 Quick Equations with Variables on Each Side Practice Problems

/5

Equations with Variables on Both Sides Quiz

Click Start to begin the practice quiz!

1 / 5

Solve the equation for x.

2x - 3 = 11x - 21

2 / 5

Solve the equation for x.

3x - 53 = 5x + 13

3 / 5

Solve the equation for x.

4x - 19 = x + 11

4 / 5

Solve the equation for x.

-22 - x = 10 - 3x

5 / 5

Solve the equation for x.

55x + 19 = -5x - 41

Your score is

0%

 

Equations with Variables on Both Sides Word Problems

Word problems are a common way to test a student’s understanding of equations with variables on both sides. These types of problems can be tricky, but with practice, students can become proficient in solving them.

When solving word problems with variables on both sides, it is important to remember that the goal is to isolate the variable on one side of the equation. This is typically done by using the properties of equality to move variables from one side to the other.

To help students understand how to solve equations with variables on both sides, teachers often use real-world scenarios to create word problems. For example, a problem might ask how long it will take two leaking containers to have the same amount of water if one container has a leak rate of 6 ml per minute and the other has a leak rate of 10 ml per minute.

To solve this problem, students would need to write an equation that represents the situation, such as:

800 – 6x = 1000 – 10x

Where x represents the number of minutes it takes for the containers to have the same amount of water. From here, students would use the properties of equality to isolate the variable, x, on one side of the equation.

Another common type of word problem with variables on both sides involves distance, rate, and time. For example, a problem might ask how long it takes two runners to meet if one runner is running at a speed of 6 miles per hour and the other is running at a speed of 8 miles per hour.

To solve this problem, students would need to write an equation that represents the situation, such as:

6x + 6 = 8x

Where x represents the number of hours it takes for the runners to meet. From here, students would use the properties of equality to isolate the variable, x, on one side of the equation.

Overall, word problems with variables on both sides can be challenging, but with practice and a solid understanding of the properties of equality, students can become proficient in solving them.

 

How to do Equations with Variables on Both Sides FAQ

How do you solve multi-step equations with variables on both sides?

To solve multi-step equations with variables on both sides, start by simplifying the equation using the distributive property, combining like terms, and moving all the variable terms to one side of the equation. Then, use inverse operations to isolate the variable and solve for its value.

What is the process for solving equations with variables on both sides?

The process for solving equations with variables on both sides involves simplifying the equation, moving all the variable terms to one side, and then isolating the variable using inverse operations. It is important to perform the same operation on both sides of the equation to maintain balance.

Can you provide an example of solving an equation with variables on both sides?

Sure! An example of solving an equation with variables on both sides is:

2x + 5 = 3x – 4

First, move all the variable terms to one side by subtracting 2x from both sides:

5 = x – 4

Then, isolate the variable by adding 4 to both sides:

9 = x

Therefore, x = 9.

What are some common mistakes to avoid when solving equations with variables on both sides?

Some common mistakes to avoid when solving equations with variables on both sides include forgetting to perform the same operation on both sides, combining unlike terms, and distributing incorrectly. It is important to check your work and simplify as much as possible before moving on to the next step.

Is there a specific order to follow when solving equations with variables on both sides?

Yes, the specific order to follow when solving equations with variables on both sides is to simplify the equation, move all the variable terms to one side, and then isolate the variable using inverse operations. It is important to maintain balance by performing the same operation on both sides of the equation.

How do you check your answer when solving equations with variables on both sides?

To check your answer when solving equations with variables on both sides, substitute the value of the variable back into the original equation and simplify. If the equation is true, then the solution is correct.

How to solve an equation with variables on both sides?

To solve an equation with variables on both sides, simplify the equation, move all the variable terms to one side, and then isolate the variable using inverse operations. It is important to perform the same operation on both sides of the equation to maintain balance.

What is an example of a linear equation with variables on both sides?

An example of a linear equation with variables on both sides is:

3x – 2 = 2x + 5

This equation has variables on both sides and can be solved using the process mentioned above.

 

Solving Equations with Variables on Both Sides Worksheet Video Explanation

Watch our free video on how to solve Equations with Variables on Both Sides. This video shows how to solve problems that are on our free Solving Equations with x on Both Sides worksheet that you can get by submitting your email above.

Watch the free Equations with Variables on Both Sides video on YouTube here: How to Solve Equations with Variables on Both Sides Video

Video Transcript:

In this video we’re gonna work on some solving equations with variables on both sides practice problems from our solving equations with variables on both sides worksheets. Let’s jump to number one. Our first problem on our how to solve equations with variables on both sides worksheet gives us 4x minus 19 equals x plus 11. The first step in solving this equation with variables on both sides is to get all the constants on one side together.

What we need to do is we need to add 19 here to this side plus 19 that the constant on this side will go away and that we have the constants on the same side together or only on one side. After we add 19 here the 19’s cancel and we bring down the 4 x on this side and we bring down the X on this side and then we’re going to combine 11 plus 19 which is 30. Then the next step is we need to get the variable on the same side together. In order to do that we need to subtract the X here and the reason we’re subtracting X is because we have to get the variables on the opposite side of the constant.

If we subtracted 4x and put the 4x over here that wouldn’t work because they would be on the same side of the equal sign and we don’t want to do that we want to get the X or we want to get the variables on the opposite side of the equal sign. After you subtract this X to get rid of this X here. This X goes away we have 4 X minus 1 X which is 3 X. On this side and then we have 30 on this side. This 3x is like saying 3 times X. In order to get rid of this coefficient you have to divide by 3 because the opposite of 3 times something is to divide that same number by 3. We will divide this by three the X the threes cancel and you’re left with just X on this side and then a 30 divided by 3 is 10. Our solution to our first equation with variables on both sides is x equals 10.

Alright moving on to our next problem, which is number two on our solving equations variables on both sides worksheet. We have 2x minus 3 equals 11x minus 21. In this case the first thing we need to do is we need to get the constants on the same side together. In order to do that I’m going to add 3 here so that the constant on this side of the equal sign will go away. We use positive 3 because this is minus 3 they will cancel and you’re left with 2x on this side and then you bring down your 11x here and then negative 21 plus 3 is negative 18.

The next step is to get rid of this 11x so we have to subtract 11x here, and once again the reason we’re subtracting 11x is because we have to get the X’s or the variables on one side of the equals sign and the constants on the other side of the equals sign. We subtract 11x here when you subtract 11x these X’s cancel 2x minus 9x is, I’m sorry 2x minus 11x, is negative 9x equals and then you bring down your negative 18 on this side. The last step is to divide both sides by negative 9 because the coefficient is negative 9. We have to cancel that out so you divide this side by negative 9. The negative 9s cancel and you’re left with on this side negative 18 divided by negative 9 which is positive 2. This is the second example of how to do equations with variables on both sides.

The last problem we’re going to work on on our multi step equations with variables on both sides worksheet is number five. Number five gives us 3x minus 53 equals 5x plus 13. The first step in solving this problem is to get all the constants on the same side together. We’re going to go ahead and add 53 here so that these guys will cancel and you’ll be left with 3x on this side and then you bring your 5x straight down and then 13 plus 53 is 66. Our next step is to get the variables on the opposite side of the constants.

We’re going to subtract 5x here the 5x is canceled and you have 3x minus 5x which is negative 2 x equals 66 on this side. Then your final step is to get rid of this negative 2. We have to divide this side by negative 2 whatever you do to one side you do to the other. We divide over here by negative 2 these guys cancel you’re left with just x equals 60 6 divided by negative 2 which is negative 33. That is our solution to our last problem in our equations with variable on both sides worksheet and download the solving equations with variables on both sides notes for more practice.

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Free Equations with Variables on Both Sides Worksheet

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