Multi Step Equations Worksheet, Examples, and Practice

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4 EASY tips for Solving Multi Step Equations (How to solve Multi Step Equations)

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Key Points about Multi Step Equations

Multi-step equations require more than one operation to solve.
The goal is to isolate the variable on one side of the equation while keeping the constant or number on the opposite side.
Following the correct order of operations is crucial when solving multi-step equations.

How to do Multi Step Equations

Solving Multi Step Equations happens when a linear equation has multiple Like Terms on the same side of the equal side. The first thing you must do is recognize that Like Terms exist on the same side of the equal sign. Once you have realized that the equation has Like Terms on the same side, you must Combine the Like Terms by either adding them together or subtracting them. After you Combine the Like Terms, 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. Our Solving Multi Step Equations Worksheet are very helpful when working on this topic.

Multi-step equations are a fundamental concept in algebra that is used to solve equations that require more than one operation. These equations can be a bit more complicated than one-step equations and require a bit more effort to solve. The goal of solving multi-step equations is to isolate the variable on one side of the equation while keeping the constant or number on the opposite side.

To solve multi-step equations, one needs to follow a series of steps that involve combining like terms, distributing, and simplifying the equation. It is important to note that the order of operations must be followed when solving multi-step equations. Failure to follow the correct order of operations can lead to incorrect solutions.

Learning how to solve multi-step equations is essential for anyone interested in pursuing a career in mathematics or science. It is a building block for more advanced concepts and is used in various fields such as engineering, physics, and economics. Understanding the basics of multi-step equations can also help students to develop critical thinking skills and problem-solving abilities.

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, Equations with Variables on Both Sides, Equations with the Distributive Property
Return To: Home, 8th Grade

What are Multi Step Equations?

Multi-step equations are mathematical equations that require more than one step to solve. They are composed of basic components, including variables, constants, and operations. Multi-step equations can be used to solve real-world problems, such as calculating the cost of a trip or determining the time it takes for an object to fall to the ground.

Basic Components of Equations

The basic components of an equation include variables, constants, and operations. Variables are symbols used to represent unknown values, while constants are known values. Operations are mathematical actions, such as addition, subtraction, multiplication, and division, used to manipulate these values.

In a multi-step equation, the goal is to isolate the variable on one side of the equation. To do this, you must use the inverse operation of each operation in the equation, working from left to right. The inverse operation of addition is subtraction, and the inverse operation of multiplication is division.

Types of Multi-Step Equations

There are several types of multi-step equations, including two-step equations and equations with variables on both sides. Two-step equations involve two operations and can be solved by working backwards from the final solution. Equations with variables on both sides involve variables on both sides of the equation and require more than two steps to solve.

In general, multi-step equations can be simple or complex, depending on the number of steps required to solve them. They can involve fractions, decimals, and negative numbers, making them challenging for some students. However, with practice and patience, anyone can learn to solve multi-step equations.

Solving Multi Step Equations

When faced with a multi-step equation, it may seem daunting to find the solution. However, by breaking down the equation into smaller steps, it becomes easier to solve. This section will cover three methods for solving multi-step equations: using inverse operations, order of operations, and distributive property.

Using Inverse Operations

The first step in solving a multi-step equation is to use inverse operations to isolate the variable. Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division. To isolate the variable, the inverse operation of each operation in the equation must be applied in reverse order.

For example, consider the equation 3x + 5 = 14. To isolate x, the inverse operation of adding 5 is subtracting 5 from both sides of the equation. This gives:

3x = 9

Next, the inverse operation of multiplying by 3 is dividing by 3. This gives the solution:

x = 3

Order of Operations

Another method for solving multi-step equations is to use the order of operations. The order of operations is a set of rules that dictate the order in which operations should be performed in an equation. The order of operations is:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

By following the order of operations, the equation can be simplified until the variable is isolated. For example, consider the equation 4(2x – 1) + 3 = 11. Using the order of operations, the equation can be simplified as follows:

4(2x - 1) + 3 = 11
8x - 4 + 3 = 11
8x - 1 = 11
8x = 12
x = 1.5

Distributive Property

The distributive property is another useful tool for solving multi-step equations. The distributive property states that a(b + c) = ab + ac. This means that a number outside of parentheses can be distributed to each term inside the parentheses.

For example, consider the equation 2(3x – 4) + 5 = 7x. Using the distributive property, the equation can be simplified as follows:

6x - 8 + 5 = 7x
6x - 3 = 7x
-3 = x

By using inverse operations, order of operations, and the distributive property, multi-step equations can be solved with confidence and ease.

3 Simple Multi Step Equations Examples

Multi-step equations are algebraic equations that require more than one step to solve. They can include a combination of addition, subtraction, multiplication, division, and other mathematical operations.

Steps to solve Multi Step Equations:

Combine the Like Terms of one and three by adding them together.
Subtract four from both sides so that you have the variable on one side and constants on the other.
Divide both sides by four so that you solve the equation for x equals four.

Here are some examples of multi-step equations:

Solving Two-Step Equations

Two-step equations are equations that can be solved in two steps. An example of a two-step equation is:

2x + 3 = 11

To solve this equation, first subtract 3 from both sides to isolate the variable:

2x = 8

Then, divide both sides by 2 to solve for x:

x = 4

Multi Step Equations with Variables on Both Sides

Multi-step equations with variables on both sides are equations where the variable appears on both sides of the equation. An example of a multi-step equation with variables on both sides is:

3x + 5 = 2x + 10

To solve this equation, first subtract 2x from both sides:

x + 5 = 10

Then, subtract 5 from both sides:

x = 5

Multi Step Equations with Distributive Property

Multi-step equations with distributive property are equations that require the distributive property to be used to solve them. An example of a multi-step equation with distributive property is:

2(3x + 4) - 5x = 11

To solve this equation, first distribute the 2:

6x + 8 - 5x = 11

Then, combine like terms:

x + 8 = 11

Finally, subtract 8 from both sides:

x = 3

It is important to always check the solution by plugging it back into the original equation. By doing this, one can ensure that the solution is valid.

5 Quick Multi Step Equations Practice Problems

Multi Step Equations Integers

Multi-step equations with integers involve equations with more than one operation and coefficients that are integers. These types of equations require multiple steps to solve.

Isolating Variables

The main goal in solving multi-step equations is to isolate the unknown variable on one side of the equation while keeping the constant or number on the opposite side. This can be done by using inverse operations to undo each operation in the equation until the variable is alone.

For example, consider the equation 3x + 5 = 17. To isolate x, we can start by subtracting 5 from both sides of the equation, which gives us 3x = 12. Then, we can divide both sides by 3 to get x = 4.

Combining Like Terms

Another important aspect of solving multi-step equations is combining like terms. Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, but 3x and 5y are not.

To combine like terms, we add or subtract their coefficients while keeping the variable the same. For example, consider the equation 2x + 3x – 5 = 10. To combine the like terms 2x and 3x, we add their coefficients to get 5x. Then, we add 5 to both sides of the equation to get 5x = 15. Finally, we divide both sides by 5 to get x = 3.

In summary, solving multi-step equations with integers involves isolating variables and combining like terms. By using inverse operations and combining like terms, one can solve these types of equations and find the value of the unknown variable.

Multi Step Equations with Fractions

Multi-step equations with fractions can be challenging, but with the right approach, they can be solved easily. In this section, we will discuss how to solve multi-step equations with fractions, including equations with exponents.

Equations with Fractions

To solve an equation with fractions, the first step is to get rid of the fractions. This can be done by finding the least common denominator (LCD) of all the fractions in the equation and multiplying both sides of the equation by that LCD. This will eliminate the fractions from the equation, making it easier to solve.

For example, consider the equation:

2/3x + 1/4 = 5/6

To solve this equation, we need to find the LCD of 2/3 and 1/4, which is 12. We then multiply both sides of the equation by 12:

12(2/3x + 1/4) = 12(5/6)

Simplifying this equation gives us:

8x + 3 = 10

We can then solve for x:

8x = 7
x = 7/8

Equations with Exponents

Equations with exponents can also be solved using a multi-step approach. The first step is to simplify any exponents in the equation. This can be done using the rules of exponents, such as:

a^m * a^n = a^(m+n)
(a^m)^n = a^(mn)
a^(-m) = 1/a^m

Once the equation has been simplified, we can then solve it using the same methods as before.

For example, consider the equation:

3^(2x-1) = 27

We can simplify this equation by writing 27 as 3^3:

3^(2x-1) = 3^3

We can then equate the exponents:

2x - 1 = 3

Solving for x gives us:

2x = 4
x = 2

In conclusion, solving multi-step equations with fractions and exponents requires a solid understanding of the underlying principles. By following the steps outlined above, these equations can be solved with confidence and accuracy.

Multi Step Equations Steps FAQ

How can the distributive property be used to solve multi-step equations?

The distributive property can be used to simplify expressions and solve multi-step equations. It allows you to remove parentheses by distributing the value outside the parentheses to each term inside. For example, if you have the equation 3(x + 2) = 15, you can use the distributive property to get 3x + 6 = 15. From there, you can solve for x.

What is the process for solving multi-step equations with two variables?

To solve multi-step equations with two variables, you need to isolate one variable on one side of the equation and then solve for the other variable. This can be done by using the same methods used to solve regular multi-step equations, such as combining like terms, distributing, and simplifying.

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

To solve multi-step equations with variables on both sides, you need to combine like terms on each side of the equation, then move all the variable terms to one side and all the constant terms to the other side. Then, you can solve for the variable using the same methods used to solve regular multi-step equations.

What are the steps to solve a multi-step equation?

The steps to solve a multi-step equation include simplifying each side of the equation, combining like terms, distributing if necessary, moving all variable terms to one side of the equation and all constant terms to the other side, and then solving for the variable.

Can you provide an example of a multi-step equation?

Sure! An example of a multi-step equation is 2x + 3 = 7x - 5. To solve this equation, you would start by simplifying each side of the equation, then combining like terms, and finally solving for x.

What is the method for solving a 3-step equation?

The method for solving a 3-step equation is the same as for any multi-step equation. You need to simplify each side of the equation, combine like terms, distribute if necessary, move all variable terms to one side of the equation and all constant terms to the other side, and then solve for the variable.

What is an example of a multiple step equation?

An example of a multiple step equation is 4x - 3(x + 2) = 5x + 1. To solve this equation, you would start by distributing the -3 to get 4x - 3x - 6 = 5x + 1. Then, you would simplify each side of the equation, combine like terms, and solve for x.

What grade level is multi-step equations?

Multi-step equations are typically taught in middle school or high school math classes, depending on the curriculum and the level of the class.

Solving Multi Step Equations Worksheet Video Explanation

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

Watch the free Multi Step Equation Examples video on YouTube here: Multi Step Equations Worksheet Video

Video Transcript:

In this video we’re going to show you some problems from our multi step equations worksheet with answers.

Our first problem in our multi step equation worksheet gives us 1 plus 4x plus 3 equals 20. The first step in solving this multi-step equation is to combine like terms. What we’re going to do is we’re going to go ahead and combine the constants because those are the two like terms that are on the same side of the equation together, after we combine these we’ll do 1 plus 3, which gives us 4. We have to bring down the 4x which is also on this side and then the equals 20 which is on the other side. All we did in this step is we combined the like terms of the constant 1 and the constant 3. We did 1 plus 3 and we got 4 then we brought everything else straight down.

The next step is to go ahead and get our constants on one side of the equation sign and our variable with the coefficient on the other. In this case we’re going to subtract 4x or I’m sorry we’re going to subtract 4 from this side, whatever you do to one side you also have to do the other. We’re going to subtract 4, the 4’s on this side cancel and you’re left with just 4x and then 20 minus 4 on this side is 16, and then finally the last step is to divide. This is like 4 times X. The opposite of 4 times X is 2/4 and then whatever you do to one side you also have to do to the other. On this side the fours cancel and you’re left with just X and then over here we have 16 divided by 4 which of course is 4. Our answer is x equals 4.

Our next problem in our multi-step equations worksheet gives us x plus 15 plus x equals 55. Now this time when we combine like terms instead of combining constants we’re going to combine variables. The two like terms on this side of the equation that are same are X and X. When we add one X plus one X that will give us two x’s or two x and then you bring down your positive fifteen and you bring down your equals 55. Then the next step in this multi-step equation is to get our 15 over on this side of the equation that we’re left with just the variable on this side.

In order to get our plus or in order to get rid of our plus 15 we’re going to subtract 15. Minus 15 here and then minus 15 here, these will cancel and we have two X on this side equals 55 minus 15 which is 40. And then finally our last step is to get rid of this coefficient of two. This is like two times X. We’re going to divide and then on this side we’re also going to divide by two. The twos will cancel you have X on this side and then 40 divided by two is 20. Our answer to this multi-step equation is x equals 20.

The last problem we’re going to work on on our multi-step equation is problem eight problem. Eight gives us negative 8 equals 10 plus 8x minus 18. In the case of number eight our like terms are the two terms we’re going to combine this time. Our 10 and negative 18 when you add 10 minus 18 or 10 plus negative 18 together you will get negative 8, then you bring down your 8x your equal sign and your negative 8 on this side. Then the next step is we have to get 8x on this side of the equation by itself. We’re going to go ahead and add 8 here so that the negative 8 in the positive eight will cancel and then whatever you do to one side you do to the other.

You add 8 to the other side these guys cancel and you bring down your 8x on this side. Over here you have negative 8 plus 8 which is zero. Then the final step is to divide this side by eight because this is like 8 times x. To get rid of that 8 times X we divide by 8 and then you have to also divide this side by 8. Of course the 8’s cancel and you’re left with just X and then 0 divided by 8 is 0. Our last answer for our last problem on our multi-step equations worksheet is as 0 equals x. Try all the practice problems by downloading the free multi step equations worksheet 8th grade above.