Two Step Equations Worksheet, Examples, and Practice

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Two Step Equations | 8th Grade | Mathcation

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Key Points about Two Step Equations

Two-step equations are algebraic equations that can be solved in two steps.
They involve two operations that can be performed to isolate the variable on one side of the equation.
Two-step equations are used extensively in real-world applications, such as calculating interest rates and determining the cost of goods.

What are Two Step Equations?

Solving Two Step Equations involves primarily two steps, hence the name “Two Step Equations.” Solving Two Step Equations involved using properties of equality. The first step in solving two step equations is to get all of the constants (numbers) on one side of teh 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 into the equation for the variable.

Two-step equations are an essential component of algebra that every student must learn. A two-step equation is an algebraic equation that can be solved in two steps, making it a fundamental concept in mathematics. The equation involves two operations that can be performed to isolate the variable on one side of the equation.

In a two-step equation, the variable is multiplied or divided by a number and then added or subtracted to isolate it. The goal is to get the variable on one side of the equation and the constants on the other side. These equations are used extensively in real-world applications, such as calculating interest rates, determining the cost of goods, and solving geometric problems.

Common Core Standard: 8.EE.C.7
Basic Topics: Combining Like Terms, Distributive Property, One Step Inequalities, Two Step Inequalities, Multi Step Inequalities
Related Topics: Multi Step Equations, Equations with Variables on Both Sides, Equations with the Distributive Property
Return To: Home, 8th Grade

Solving Two Step Equations

Two Step Equations Definition

Two-step equations are algebraic equations that can be solved in exactly two steps and give the final value of the variable in two steps. Generally, two-step equations are of the form ax + b = c, where a, b, c are real numbers.

Definition of Variables

Variables are letters or symbols that represent unknown values in an equation. In a two-step equation, variables are used to find the value of the unknown variable. For example, in the equation 2x + 3 = 7, x is the variable that represents the unknown value.

Understanding the Equal Sign

The equal sign in a two-step equation indicates that the expressions on both sides of the equal sign are equal. To solve a two-step equation, one must perform the same operation on both sides of the equation until the variable is isolated on one side of the equal sign.

For example, to solve the equation 2x + 3 = 7, one would first subtract 3 from both sides to get 2x = 4. Then, one would divide both sides by 2 to get x = 2.

In summary, two-step equations are algebraic equations that can be solved in exactly two steps. Variables are used to represent unknown values in an equation, and the equal sign indicates that the expressions on both sides of the equal sign are equal.

Solving Two Step Equations

When it comes to solving two-step equations, there are a few steps that need to be followed. This section will cover the process of solving two-step equations, including isolating the variable and checking the solution.

Isolating the Variable

The first step in solving two-step equations is to isolate the variable. This means getting the variable by itself on one side of the equation. To do this, you need to use inverse operations. For example, if the equation is 2x + 3 = 11, you can isolate the variable by subtracting 3 from both sides of the equation. This gives you 2x = 8. Then, you can isolate x by dividing both sides by 2, which gives you x = 4.

Checking Your Solution

Once you have solved for the variable, it is important to check your solution. This means plugging your answer back into the original equation to make sure it works. If the equation is still true after you plug in your answer, then you have found the correct solution.

It is important to note that sometimes an equation may have no solution or an infinite number of solutions. For example, the equation 2x + 3 = 2x + 5 has no solution because there is no value of x that will make the equation true. On the other hand, the equation 2x = 2x has an infinite number of solutions because any value of x will make the equation true.

Overall, solving two-step equations requires isolating the variable and checking the solution. By following these steps, you can find the correct solution to any two-step equation.

Two Step Equations Worksheet Solution

4 Simple Two Step Equations Examples

Two step equations are mathematical equations that require two operations to solve for the variable.

Steps for solving the problem above:

First step is to add nine to both sides of the equation.
Second step is to divide both sides by nine.
Third step is to solve the equation for x equals two.

Here are some examples of two step equations:

Example 1

Solve the equation: 3x + 4 = 19

Step 1: Subtract 4 from both sides of the equation to isolate the variable x. 3x = 15

Step 2: Divide both sides of the equation by 3 to solve for x. x = 5

Therefore, the solution to the equation 3x + 4 = 19 is x = 5.

Example 2

Solve the equation: 2y – 8 = 10

Step 1: Add 8 to both sides of the equation to isolate the variable y. 2y = 18

Step 2: Divide both sides of the equation by 2 to solve for y. y = 9

Therefore, the solution to the equation 2y – 8 = 10 is y = 9.

Example 3

Solve the equation: 5z/2 + 7 = 17

Step 1: Subtract 7 from both sides of the equation to isolate the variable z. 5z/2 = 10

Step 2: Multiply both sides of the equation by 2/5 to solve for z. z = 4

Therefore, the solution to the equation 5z/2 + 7 = 17 is z = 4.

Example 4

Solve the equation: 6a – 3 = 33

Step 1: Add 3 to both sides of the equation to isolate the variable a. 6a = 36

Step 2: Divide both sides of the equation by 6 to solve for a. a = 6

Therefore, the solution to the equation 6a – 3 = 33 is a = 6.

These examples demonstrate how to solve two step equations by performing two operations in order to isolate the variable. Practice is key to mastering two step equations, and with enough practice, solving these equations will become second nature.

5 Quick Two Step Equations Practice Problems

Two Step Equations Steps

To solve a two-step equation, there are two main steps that need to be followed. These steps are Addition and Subtraction, and Multiplication and Division.

Addition and Subtraction

The first step is to add or subtract both sides of the equation by the same number. This is done to isolate the variable on one side of the equation. For example, if the equation is 2x + 5 = 11, the first step would be to subtract 5 from both sides of the equation. This would give the equation 2x = 6.

Multiplication and Division

The second step is to multiply or divide both sides of the equation by the same number. This is done to solve for the variable. For example, if the equation is 2x = 6, the second step would be to divide both sides of the equation by 2. This would give the equation x = 3.

It is important to remember that when multiplying or dividing both sides of the equation by a negative number, the direction of the inequality sign must be flipped. For example, if the equation is -2x + 5 = 11, the first step would be to subtract 5 from both sides of the equation. This would give the equation -2x = 6. The second step would be to divide both sides of the equation by -2. However, since we are dividing by a negative number, we must flip the direction of the inequality sign. This would give the equation x <= -3.

Overall, solving a two-step equation involves following these two main steps of Addition and Subtraction, and Multiplication and Division. By isolating the variable on one side of the equation, and then solving for the variable, one can find the solution to the equation.

Two Step Equations with Fractions and Decimals

Two-step equations with fractions and decimals are equations that require two operations to solve and involve fractions or decimals. These types of equations can be tricky to solve, but with the right approach, they can be solved with ease.

Equations with Fractions

When solving two-step equations with fractions, the first step is to simplify the fractions by finding a common denominator. This can be done by multiplying both the numerator and denominator of each fraction by the same number. Once the fractions are simplified, the equation can be solved using the same steps as a regular two-step equation.

For example, consider the equation: 2/3x + 1/4 = 5/6. To solve this equation, the first step is to simplify the fractions by finding a common denominator. In this case, the common denominator is 12. So, we multiply the first fraction by 4/4 and the second fraction by 3/3 to get 8/12x + 3/12 = 10/12. Now, we can solve the equation by subtracting 3/12 from both sides and then multiplying both sides by 12/8 to get x = 5.

Equations with Decimals

When solving two-step equations with decimals, the first step is to get rid of any decimals by multiplying both sides of the equation by a power of 10 that will convert the decimals to whole numbers. Once the decimals are eliminated, the equation can be solved using the same steps as a regular two-step equation.

For example, consider the equation: 0.5x + 1.2 = 3.7. To solve this equation, the first step is to get rid of the decimals by multiplying both sides by 10. This gives us 5x + 12 = 37. Now, we can solve the equation by subtracting 12 from both sides and then dividing both sides by 5 to get x = 5.

Simplifying Fractions

When working with fractions, it is important to simplify them as much as possible. This can be done by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by it. For example, if we have the fraction 8/12, we can simplify it by finding the GCF of 8 and 12, which is 4. So, we divide both the numerator and denominator by 4 to get 2/3.

Common Denominator

When working with fractions, it is important to find a common denominator before adding or subtracting them. This can be done by finding the least common multiple (LCM) of the denominators and multiplying each fraction by the appropriate factor to make the denominators the same. For example, if we have the fractions 1/3 and 2/5, we can find the LCM of 3 and 5, which is 15. So, we multiply the first fraction by 5/5 and the second fraction by 3/3 to get 5/15 and 6/15, respectively. Now, we can add the fractions to get 11/15.

Two Step Equations Word Problems

Two-step equations word problems are mathematical problems that involve two-step equations expressed using words instead of just numbers and mathematical symbols. In other words, these are problems that require two different operations to be performed to solve them. They are just a bit more complicated than one-step equations with word problems and they demand just a bit more effort to solve.

To solve two-step equations word problems, one needs to follow a few simple steps. The first step is to identify the unknown variable, which is usually denoted by a letter. The second step is to translate the word problem into an equation. The third step is to simplify the equation by applying the order of operations. Finally, one needs to solve for the unknown variable by isolating it on one side of the equation.

Here’s an example of a two-step equation word problem: “Mindy and Troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and Troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake there were in total. Find the total number of pieces of cake.”

To solve this problem, one can follow the steps mentioned above. Let’s denote the total number of pieces of cake by “c”. Then, we can write the equation as:

3 + (1/4)c = 9

Simplifying the equation by multiplying both sides by 4, we get:

12 + c = 36

Solving for “c”, we get:

c = 24

Therefore, there were 24 pieces of cake in total.

In conclusion, two-step equations word problems are a bit more challenging than one-step equations with word problems, but they can be solved by following a few simple steps.

How to Solve Two Step Equations

Two-step equations are algebraic equations that require two steps to solve. This section will explain how to solve two-step equations with whole numbers and integers.

Solving with Whole Numbers

To solve a two-step equation with whole numbers, follow these steps:

Isolate the variable term by adding or subtracting the constant term from both sides of the equation.
Isolate the variable by dividing or multiplying both sides of the equation by the coefficient of the variable.

For example, to solve the equation 5x + 2 = 17, start by subtracting 2 from both sides to get 5x = 15. Then, divide both sides by 5 to get x = 3.

Solving with Integers

Solving two-step equations with integers is similar to solving with whole numbers, but it requires extra attention to signs. Follow these steps:

Isolate the variable term by adding or subtracting the constant term from both sides of the equation.
Isolate the variable by dividing or multiplying both sides of the equation by the coefficient of the variable.

For example, to solve the equation -2x + 5 = -11, start by subtracting 5 from both sides to get -2x = -16. Then, divide both sides by -2 to get x = 8.

It is important to remember that when multiplying or dividing both sides of an equation by a negative number, the inequality sign must be flipped.

In summary, solving two-step equations can be done by isolating the variable term and then isolating the variable itself. When solving with integers, extra attention must be paid to the signs. By following these steps, anyone can solve two-step equations with confidence.

How to do Two Step Equations FAQ

How do you solve two-step equations?

To solve two-step equations, you need to isolate the variable by performing two operations. First, you need to undo the addition or subtraction, and then you need to undo the multiplication or division. To do this, you need to use inverse operations.

What are some examples of two-step equations?

An example of a two-step equation is 3x + 2 = 14. Another example is 4y – 7 = 5.

What is the process for solving two-step equations?

The process for solving two-step equations is to isolate the variable by performing inverse operations. First, undo the addition or subtraction, and then undo the multiplication or division.

What are the steps to solve multi-step equations?

The steps to solve multi-step equations are similar to those for two-step equations, but they involve more than two operations. You need to isolate the variable by performing inverse operations, starting with the operations that are furthest from the variable.

Can you provide a worksheet for solving two-step equations?

Yes, there are many worksheets available online that can help you practice solving two-step equations. One example is this worksheet from Mathcation.

What is the difference between one-step and two-step equations?

The main difference between one-step and two-step equations is the number of operations required to isolate the variable. One-step equations only require one operation, while two-step equations require two operations.

What is an example of a 2 step algebra equation?

An example of a 2 step algebra equation is 2x + 3 = 11.

What is a 2 step word equation?

A two-step word equation is a word problem that can be translated into a two-step algebra equation. For example, “If John has 4 apples and gives away 2, how many apples does he have left?” can be translated into the two-step equation 4 – 2 = x.

Two Step Equations Worksheet Video Explanation

Watch our free video on how to solve Two Step Equations. This video shows how to solve problems that are on our free 2 Step Equations worksheet that you can get by submitting your email above.

Watch the free Two Step Equations video on YouTube here: Two Step Equations Worksheet

Video Transcript:

This video is about solving two step algebra equations.

Here’s our 2 step equations worksheet, let’s do some two step equations examples problems from it. First practice problem gives us 9 x minus 9 equals 9. The first thing we have to do when solving two-step equations is we have to get rid of this minus 9. We’re going to go ahead and add 9 to both sides. When we add 9 here, this minus sign this plus 9 will cancel and we’ll be left with 9 X on this side is equal to 9 plus 9 on this side, which is 18. Then the next step is we need to get rid of this 9 x this 9 x is like saying 9 times X. The opposite of multiplication is to divide, we’re going to go ahead and divide this by 9, and whatever you do to one side you have to do the other, we’re also going to divide this by 9. The nines over here will cancel and then 18 divided by 9 equals 2 and then like I said the 9s cancel on this side. We have just X and our final answer is x equals 2.

We’re going to jump to number 3 on our 2 step equations worksheets. Number 3 gives us 134 equals negative 10 X plus 14. Once again we have to get the negative 10 x on one side of the equation and the constants on the other side. We have to get rid of this plus 14 or we have to move the plus 14 over to this side. We’re going to subtract 14 here because the opposite of plus 14 is minus 14, whatever you do to one side you also have to do the other. We’re also going to subtract 14 from this side. These will cancel over here we have 134 minus 14 which is 120 equals negative 10x.

You bring that straight down and this is like saying negative 10 times X or the coefficient on X would be negative 10. It’s like negative 10 times X, you have to divide this by negative 10 because the opposite of negative 10 times something is 2 divided by negative 10. Whatever you do to one side you also do the other. You also divide this side by negative 10 over here the negative 10 is canceled and you’re left with just X and then on this side you do 120 divided by negative 10 which would be negative 12. Our solution is negative 12 equals x.

The last 2 step equations examples we’re going to go over on our two step equation worksheet is number 7, which is 31 equals negative x minus 8. Our first step is we have to get rid of this negative 8 because it’s on the same side as the variable and we need to get all the constants on the same side together. The opposite of negative 8, or subtract 8, is to add 8. We’re going to add 8 to both sides, these will cancel, we’re left with 39 equals negative x. Then the final step and the reason we included this in our example video for two-step equations is to get rid of this negative 1x.

In other words negative X is not the solution because it’s still not simplified, you have to make this a positive x. Even though it’s not written this is really like saying negative 1x. This is really like having a negative 1x here. In order to get rid of this negative 1 is to divide by negative 1. We divide here by negative 1 and we also divide here by negative 1. Now the negative ones cancel and you have just x over here and then 39 divided by negative 1 is negative 39 and that’s your answer. You can try all of these practice problems by downloading the free two step algebra equations worksheets above.