Solving One Step Equations Worksheet, Examples, Explanation

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Solving One Step Equations | How to Solve One Step Equations | 6th Grade

Key Points about Solving One Step Equations

  • One step equations involve solving equations with only one arithmetic operation.
  • To solve one step equations, students must perform the inverse operation of the arithmetic operation being used on the variable.
  • One step equations are used in real-world scenarios and are essential for students to understand in order to progress in their mathematical education.

Solving One Step Equations

One step equations are a fundamental concept in algebra that involve solving equations with only one arithmetic operation. These equations can be solved quickly and easily by performing the inverse operation of the arithmetic operation being used on the variable. One step equations are a building block for more complex algebraic concepts and are essential for students to understand in order to progress in their mathematical education.

To solve a one step equation, students must determine what operation is being performed on the variable and then perform the inverse operation to isolate the variable. For example, if the equation is 3x + 5 = 14, students would subtract 5 from both sides of the equation to get 3x = 9, and then divide both sides by 3 to get x = 3. One step equations can involve addition, subtraction, multiplication, or division, and can include fractions and decimals.

One step equations are used in many real-world scenarios, such as calculating the cost of an item on sale or determining the amount of time it takes to travel a certain distance. Understanding how to solve one step equations is an important skill that students will use throughout their academic and professional careers.

One Step Equations are algebraic equations that can be solved in only one step. Each equation will have numbers and a variable. The variable is a representation of an unknown number that you are trying to figure out. In order to find the number that the variable is equal to you have to use addition, subtraction, multiplication, or division. When you are deciding which operation to use, you have to use the opposite operation that is being used in the equation. For example, the opposite of addition is subtraction, so if you needed to solve an equation with an addition sign, you would use subtraction because it is the opposite of addtion. You know the equation has been solved when you have a final solution of the variable equals a number.

Common Core Standard: 6.EE.7
Related Topics: Evaluating Expressions, Equivalent Expressions, Combining Like Terms, Distributive Property with Variables
Return To: Home, 6th Grade

Solving One Step Equations

What are One Step Equations?

A one-step equation is a type of algebraic equation that can be solved in just one step. It involves only one operation such as addition, subtraction, multiplication, or division. The goal of solving a one-step equation is to find the value of the variable that makes the equation true.

In a one-step equation, the variable is always multiplied or divided by a constant, and the inverse operation is applied to isolate the variable. For example, if the equation is 2x = 8, the inverse operation is division, and the equation can be solved by dividing both sides by 2. The solution is x = 4.

One-step equations are a fundamental concept in algebra and are used to solve a wide variety of problems. They are commonly used in real-life situations such as calculating the cost of an item on sale, finding the distance traveled by a car, or determining the amount of time needed to complete a task.

To solve a one-step equation, it is important to understand the concept of inverse operations. Inverse operations are opposite operations that undo each other. For example, addition and subtraction are inverse operations, as are multiplication and division. By applying inverse operations to both sides of the equation, the variable can be isolated and the solution can be found.

One-step equations can involve integers, decimals, fractions, and coefficients. The coefficient is the number that is multiplied by the variable. To solve an equation with a coefficient, the inverse operation is applied to both sides of the equation, and the coefficient is divided or multiplied accordingly. The goal of solving a one-step equation is to create a balanced mathematical sentence where the variable is isolated and the equation is true.

 

How to Solve One Step Equations

One step equations are algebraic equations that can be solved in only one step. The equation will have a variable, which represents an unknown value, and a constant, which is a number you need to add, subtract, multiply, or divide from the variable to equal a certain sum or difference. In order to solve one step equations, you need to do the inverse (opposite) of whatever operation is being performed on the variable, so you get the variable by itself.

Addition and Subtraction

To solve one step equations that involve addition and subtraction, you need to perform the opposite operation on both sides of the equation. For example, consider the equation x + 5 = 12. To solve for x, you need to subtract 5 from both sides of the equation. This will give you x = 7.

Multiplication and Division

To solve one step equations that involve multiplication and division, you need to perform the opposite operation on both sides of the equation. For example, consider the equation 4x = 20. To solve for x, you need to divide both sides of the equation by 4. This will give you x = 5.

Examples

Let’s look at some examples of one step equations:

  • 3x = 9: To solve for x, you need to divide both sides of the equation by 3. This will give you x = 3.
  • 7 - y = 3: To solve for y, you need to subtract 7 from both sides of the equation. This will give you -y = -4. Then, you need to multiply both sides of the equation by -1 to get y = 4.
  • 5z + 2 = 17: To solve for z, you need to subtract 2 from both sides of the equation. This will give you 5z = 15. Then, you need to divide both sides of the equation by 5 to get z = 3.

Coefficients and Decimals

One step equations can also involve coefficients and decimals. To solve for the variable in these equations, you need to follow the same steps as before. For example, consider the equation 0.5x + 1 = 3. To solve for x, you need to subtract 1 from both sides of the equation. This will give you 0.5x = 2. Then, you need to multiply both sides of the equation by 2 to get x = 4.

Balanced Equations

When you solve a one step equation, you should end up with a balanced equation. This means that the variable is by itself on one side of the equation, and the constant is on the other side. For example, consider the equation 2y - 6 = 2. To solve for y, you need to add 6 to both sides of the equation. This will give you 2y = 8. Then, you need to divide both sides of the equation by 2 to get y = 4. This is a balanced equation because y is by itself on one side of the equation, and 4 is on the other side.

 

One Step Equations Addition and Subtraction

One-step equations are mathematical sentences that can be solved in one step, using inverse operations. One-step equations with addition and subtraction are the simplest type of one-step equations. They involve adding or subtracting the same number from both sides of the equation to isolate the variable.

To solve a one-step equation with addition or subtraction, you need to undo the operation that is being done to the variable. For example, if the variable is being added to a number, you can subtract the same number from both sides of the equation to isolate the variable. If the variable is being subtracted from a number, you can add the same number to both sides of the equation to isolate the variable.

Here is an example of a one-step equation with addition:

x + 5 = 12

To solve for x, you need to subtract 5 from both sides of the equation:

x + 5 - 5 = 12 - 5
x = 7

The solution to the equation is x = 7.

Here is an example of a one-step equation with subtraction:

y - 8 = 3

To solve for y, you need to add 8 to both sides of the equation:

y - 8 + 8 = 3 + 8
y = 11

The solution to the equation is y = 11.

In general, the goal of solving a one-step equation is to isolate the variable on one side of the equation, with a balanced expression on the other side. A balanced expression means that the same number or variable is added or subtracted from both sides of the equation.

One-step equations with addition and subtraction can involve integers, decimals, and fractions. The coefficient of the variable can also be any number. However, the process for solving the equation remains the same: undo the operation being done to the variable by using inverse operations.

Overall, one-step equations with addition and subtraction are a fundamental concept in algebra. They provide a foundation for more complex equations and expressions.

 

One Step Equations Multiplication and Division

One-step equations involving multiplication and division are fundamental concepts in algebra. These equations are mathematical sentences that express the equality of two expressions containing variables and numbers. One-step equations with multiplication and division are solved by using inverse operations to isolate the variable.

Multiplication and division are inverse operations, which means that they undo each other. To solve a one-step equation with multiplication, divide both sides by the coefficient of the variable. To solve a one-step equation with division, multiply both sides by the reciprocal of the coefficient of the variable.

For example, consider the equation 5x = 20. To solve for x, divide both sides by 5, giving x = 4. In another example, consider the equation x/3 = 6. To solve for x, multiply both sides by 3, giving x = 18.

It is important to keep the equation balanced by performing the same operation on both sides of the equation. The goal is to isolate the variable on one side of the equation and simplify the expression on the other side.

One-step equations with multiplication and division involve integers, decimals, and fractions as coefficients. Students should be able to identify the coefficient, variable, and constant in the equation and use inverse operations to solve for the variable.

In summary, one-step equations with multiplication and division are solved by using inverse operations to isolate the variable. Multiplication and division are inverse operations that undo each other. Students should be able to identify the coefficient, variable, and constant in the equation and maintain balance by performing the same operation on both sides of the equation.

 

Solving One Step Equations Solution

3 Quick One Step Equations Examples

One-step equations are mathematical sentences that can be solved in a single step. They have only one variable and one operation. These equations are an essential part of algebra and are frequently used in solving mathematical problems. Here are some examples of one-step equations:

Example 1:

Solve for x in the following equation: 5x = 20

To solve this equation, we need to isolate the variable x on one side of the equation. We can do this by dividing both sides of the equation by 5. This gives us:

5x/5 = 20/5

x = 4

Therefore, the solution to the equation 5x = 20 is x = 4.

Example 2:

Solve for y in the following equation: 3y – 6 = 9

To solve this equation, we need to isolate the variable y on one side of the equation. We can do this by adding 6 to both sides of the equation. This gives us:

3y – 6 + 6 = 9 + 6

3y = 15

y = 5

Therefore, the solution to the equation 3y – 6 = 9 is y = 5.

Example 3:

Solve for z in the following equation: z/2 = 6

To solve this equation, we need to isolate the variable z on one side of the equation. We can do this by multiplying both sides of the equation by 2. This gives us:

z/2 × 2 = 6 × 2

z = 12

Therefore, the solution to the equation z/2 = 6 is z = 12.

One-step equations can involve integers, decimals, and fractions. They can also be used to solve real-world problems. For example, if a student has scored 80 marks out of 100 in a test, what percentage of marks did he score? The answer to this problem can be found by solving the one-step equation (80/100) × 100 = 80%.

Students can practice solving one-step equations using worksheets and exercises. These resources can help them to understand the concept of one-step equations and build their problem-solving skills.

 

5 Simple One Step Equations Practice Problems

/5

Solving One-Step Equations

Click Start to begin the practice quiz!

1 / 5

Solve the following One-Step equation:

x + 5 = 10

2 / 5

Solve the following One-Step equation:

x - 4 = 3

3 / 5

Solve the following One-Step equation:

x + 9 = 20

4 / 5

Solve the following One-Step equation:

4x = 16

5 / 5

Solve the following One-Step equation:

x - 8 = 5

Your score is

0%

 

One Step Equations with Fractions

One-step equations with fractions are mathematical sentences that involve fractions and require only one step to solve. These equations can be solved by using inverse operations, which means performing the opposite operation to both sides of the equation to isolate the variable.

To solve one-step equations with fractions, it is important to remember that the goal is to isolate the variable. This can be done by performing the inverse operation on both sides of the equation. For example, if the equation involves adding a fraction to a variable, then subtracting the same fraction from both sides of the equation will isolate the variable.

When solving one-step equations with fractions, it is also important to pay attention to the numerator and denominator of the fractions involved. Multiplying both sides of the equation by the reciprocal of the fraction can help eliminate the fraction.

Here is an example of a one-step equation with fractions:

3/4x = 6

To solve this equation, one can multiply both sides by the reciprocal of 3/4, which is 4/3.

(4/3) * (3/4x) = (4/3) * 6
x = 8

Therefore, the solution to the equation is x = 8.

In conclusion, one-step equations with fractions can be solved by using inverse operations and paying attention to the numerator and denominator of the fractions involved. By following these steps, one can isolate the variable and find the solution to the equation.

 

One Step Equations Word Problems

One step equations are mathematical sentences that involve only one operation to solve. They are commonly used in algebra to help students understand how to solve equations using basic arithmetic operations. One step equation word problems are a type of problem that requires students to use their understanding of one step equations to solve real-world problems.

Solving One Step Equations Word Problems

To solve one step equation word problems, students need to follow a few simple steps. First, they need to read the problem carefully and identify the operation that is being used. Next, they need to write an equation that represents the problem using the appropriate variables. Then, they need to solve the equation by performing the inverse operation to isolate the variable. Finally, they need to check their answer by plugging it back into the original equation to make sure it is correct.

Example

Here is an example of a one step equation word problem:

“Lisa is cooking muffins. The recipe calls for 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in?”

To solve this problem, students can follow the steps outlined above. First, they need to identify that the operation being used is addition. Next, they can write the equation:

2 + x = 7

Then, they can solve the equation by performing the inverse operation:

x = 7 – 2

x = 5

Finally, they can check their answer by plugging it back into the original equation:

2 + 5 = 7

This equation is balanced, so the answer is correct.

Integers and Decimals

One step equation word problems can involve both integers and decimals. Students need to be comfortable working with both types of numbers to solve these problems. They should also be familiar with the order of operations and how to simplify expressions.

Balanced Equations

One step equation word problems require students to create a balanced equation. This means that the equation has the same value on both sides of the equal sign. Students need to make sure that they perform the same operation on both sides of the equation to keep it balanced.

One step equation word problems are an important part of algebra. They help students develop their problem-solving skills and build a strong foundation in basic arithmetic operations. By following a few simple steps, students can solve these problems with confidence and accuracy.

 

How to Solve One Step Equations FAQ

How do you solve one-step equations?

To solve a one-step equation, you need to isolate the variable. This means that you want to get the variable by itself on one side of the equation. To do this, you need to perform the inverse operation of the operation that is currently being performed on the variable. For example, if you have the equation 3x = 12, you would divide both sides by 3 to get x = 4.

What is an example of a one step equation?

An example of a one-step equation is 2x = 8. To solve this equation, you would divide both sides by 2 to get x = 4.

What are the 4 rules of solving one step equations?

The four rules of solving one-step equations are:

  1. If you have an equation of the form x + b = c, subtract b from both sides to get x by itself.
  2. If you have an equation of the form x - b = c, add b to both sides to get x by itself.
  3. If you have an equation of the form ax = c, divide both sides by a to get x by itself.
  4. If you have an equation of the form x/a = c, multiply both sides by a to get x by itself.

What is an example of a one step equation in math?

An example of a one-step equation in math is 4x = 20. To solve this equation, you would divide both sides by 4 to get x = 5.

What are some common mistakes when solving one-step equations?

Some common mistakes when solving one-step equations include:

  • Forgetting to perform the inverse operation on both sides of the equation.
  • Forgetting to simplify both sides of the equation before solving.
  • Making a sign error when performing the inverse operation.
  • Making a calculation error when performing the inverse operation.

How can you check your answer when solving one-step equations?

You can check your answer when solving one-step equations by plugging it back into the original equation and seeing if it makes the equation true. For example, if you solved the equation x + 3 = 7 and got x = 4, you could plug 4 back into the equation to get 4 + 3 = 7, which is true.

 

One Step Equations Worksheet Video Explanation

Watch our free video on how to solve 1 Step Equations. This video shows how to solve problems that are on our free One Step Algebra Equation Worksheets that you can get by submitting your email above.

Watch the free One Step Equation Practice video on YouTube here: Solving One Step Equation Video

Video Transcript:

This video is about solving one-step equations. You can get the one step equation worksheet used in this video for free by clicking on the link in the description below.

One-step equations are equations that you can solve in one step, hence the name easy one step equations. Typically, when solving one-step equations, you will either use addition, subtraction, multiplication, or division. The trick in solving one-step equations is to keep the equation balanced. This means that whatever you do to one side you also have to do to the other side. Think of the equal sign as sort of a divider represents two equal sides and that the two sides have to remain balanced. If you perform an operation on one side you also have to do the same exact operation on the other side.

If you look at our example here, we have x plus 3 equals 4. We are trying to solve for x. We want to know what x is equal to. In order to solve for x we have to undo this plus three. This plus three is in our way and we have to get rid of it. In order to get rid of this plus three you have to undo it or do the opposite of plus three. In this case the opposite of plus three is minus three so in order to get rid of plus three we’re going to do minus three. The reason we’re doing that is so the threes on this side go away. Remember our equal sign separates the equation into two sides that must remain equal. Whatever you do on one side you also have to do to the other side of the equal sign. In this case since we did minus three on this side, we also have to do minus three on the other side. You now have 4 minus 3 which is 1. We have 1 on this side and then all that’s left on our left side is x. This plus 3 is now canceled because we did minus three and all that’s left over here is x and four minus three is one so our solution is x equals one. I know that we’re done simplifying when we have x equals a number on the other side of the equal sign. Let’s do a couple practice problems on our one-step equations worksheet.

The first problem we’re going to complete on our one step equation worksheet for showing you how to solve one-step equations is problem one. This problem gives us x plus one equals four. Now we know that whatever we do to one side of the equation we also have to do the other. In this case we have x minus 1 equals 4. We have to do the opposite of -1 because we’re trying to get x on this side by itself. In order to get x by itself we have to get rid of this minus 1. The opposite of minus 1 is plus 1. We’re going to do plus 1 here so that this minus 1 and this plus 1 cancel and then whatever you do to one side of the equal sign you also have to do to the other. We’re also going to do a plus 1 on this side on the left side all that’s left is x. Now we have our x we have our equal sign in the middle that we bring straight down finally we’re going to do 4 plus 1 to get our solution of 5.  The solution to this one step equation is x equals 5.

The next problem we’re going to complete on the one step equations worksheet 6th grade is number two which gives us three x equals twenty-one. Now three x is like saying three times x. This is like saying three times x equals twenty one. The opposite of 3 times something or opposite of multiplying something times 3 is to divide by 3. We’re going to divide this side by 3 so that 3 divided by 3 will cancel. The 3s will cancel and we’re left with just x on this side and then whatever you do to one side you also have to do the other. We also have to divide this side by 3 and 21 divided by 3 is equal to 7. Our solution is x equals 7.

The last problem we’re going to complete on our one step equations worksheets is number seven. This problem gives us x minus 8 equals two. Now the opposite of minus eight is plus eight. We’re trying to get rid of this minus eight because we want x by itself on one side so we’re going to plus eight on this side and we’re also going to do plus 8 on the other side because whatever you do to one side you also have to do the other. This minus 8 and this plus 8 cancel they go away and we’re left with x equals and then two plus eight on the other side which is ten. Our solution to number seven is x equals ten. I hope this video was helpful for teaching you solving one-step equations. Try all the practice problems by downloading the free one step equations worksheets above.

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Free One Step Equations Worksheet

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