What is an example of a one step equation?

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

An equation is a mathematical statement that demonstrates the equality of two expressions. You will frequently work with equations in algebra where a variable represents an unknown value. To solve these equations, it would be best to determine the variable’s value. To find the unknown value in a one-step equation, you only need to perform one operation; hence, this problem is the simplest to solve.

This article will teach us about one-step equations and explain how to solve cases using various examples.

What is a One-Step Equation?

Definition

An algebraic equation that only requires one step to solve is known as a one-step equation. Once the equation has been solved, we can find the value of the variable that makes the statement true.

We can use addition, subtraction, multiplication, or division to solve a one-step equation.

Types of One-Step Equations

The following are the different types of one-step equations:

1. One-step equations with subtraction

Examples: 

1. One-step equations with addition

Examples: 

1. One-step equations with division

Examples: 

1. One-step equations with multiplication

Examples: 

How do you solve one-step equations?

When solving one-step equations, we conduct the opposite operation from that applied to the variable to obtain the variable by itself.

These are the inverse operations:

Addition and Subtraction
Multiplication and Division

Let us say, for example, use subtraction when there is addition, use addition when there is subtraction, use multiplication when there is division, and vice versa.

Important: Any changes you make to one side of the equation must also be made to the other side. You have just solved the equation if you can isolate the variable by itself so that the variable has a +1 coefficient, and the constant is on the opposite side.

Solving One-Step Equations with Addition

To solve a one-step equation with addition of a number, we must subtract this number from both sides of the equation.

Examples

Example 1

Solve the one-step equation: x + 5 = 18.

Solution

In this example, x has 5 added to it. Since we want to isolate the variable x on the left-hand side of the equation, we will perform the inverse operation and subtract 5 from both sides of the equation. Hence, we have,

x + 5 = 18 Given
x + 5 – 5 = 18 – 5 Subtract 5 from both sides of the equation
x = 13 Simplify

Checking

To check the answer, substitute 13 into the variable x and see if the equation is true:

 x + 5 = 18
13 + 5 = 18
18 = 18

Since the equation is true, x = 13 is the correct solution.

Example 2

Solve for y in the following equation: y + 15 = 45.

Solution

In this example, y has 15 added to it. Since we want to isolate the variable y on the left-hand side of the equation, we will perform the inverse operation and subtract 15 from both sides of the equation. Thus, we have,

y + 15 = 45 Given
y + 15 – 15 = 45 – 15 Subtract 15 from both sides of the equation
y = 30 Simplify

Checking

To check the answer, substitute 30 into the variable y and see if the equation is true:

 y + 15 = 45
30 + 15 = 45
45 = 45

Since the equation is true, y = 30 is the correct solution.

Example 3

Solve for k: 

k + 12 = 28

Solution

In this example, k has 12 added to it. Since we want to isolate the variable k on the left-hand side of the equation, we will perform the inverse operation and subtract 12 from both sides of the equation. Hence, we have,

k + 12 = 28 Given
k + 12 – 12 = 28 – 12 Subtract 12 from both sides of the equation
k = 16 Simplify

Checking

To check the answer, substitute 16 into the variable k and see if the equation is true:

 k + 12 = 28
16 + 12 = 28
28 = 28

Since the equation is true, k = 16 is the correct solution.

Example 4

Solve the one-step equation below.

36 = k + 7

Solution

Notice that this example is slightly different from the previous examples since the variable is on the right-hand side of the equation. Remember that we need to isolate the variable on either side of the equation. Since k has 7 added to it, we will perform the inverse operation and subtract 8 from both sides of the equation. Hence, we have,

Given

36 = k + 7
Seven must be subtracted from both sides of the equation
36 – 7 = k + 7 – 7

Simplify

29 = k

Checking

To check the answer, substitute 29 into the variable k and see if the equation is true:

36 = k + 
7
36 = 29 + 7 
36 = 36

Since the equation is true, k = 29 is the correct solution.

Solving One-Step Equations with Subtraction

To solve a one-step equation with subtraction of a number, we must subtract this number from both sides of the equation.

Examples

Example 1

Solve the one-step equation: y – 6 = 25.

Solution

Since we want to isolate the variable y on the left-hand side of the equation, we will perform the inverse operation and add 6 to both sides of the equation. Hence, we have,

y – 6 = 25 Given
y – 6 + 6  = 25 + 6 Add 6 to both sides of the equation
y = 31 Simplify

Checking

To check the answer, substitute 31 into the variable y and see if the equation is true:

y – 6 = 25
31 – 6 = 25
25 = 25

Since the equation is true, y = 31 is the correct solution.

Example 2

Solve for m in the following equation: m – 21 = 35.

Solution

Since we want to isolate the variable m on the left-hand side of the equation, we will perform the inverse operation and add 21 to both sides of the equation. Thus, we have,

m – 21 = 35 Given
m – 21 + 21  = 35 + 21 Add 21 to both sides of the equation
m = 56 Simplify

Checking

To check the answer, substitute 56 into the variable y and see if the equation is true:

m – 21 = 35
56 – 21 = 35
35 = 35

Since the equation is true, m = 56 is the correct solution.

Example 3

Solve for x: 

x – 17 = 53

Solution

Since we want to isolate the variable x on the left-hand side of the equation, we will perform the inverse operation and add 17 to both sides of the equation. Hence, we have,

x – 17 = 53 Given
x – 17 + 17  = 53 + 17 Add 17 to both sides of the equation
x = 70 Simplify

Checking

To check the answer, substitute 70 into the variable x and see if the equation is true:

x – 17 = 53
70 – 17 = 53
53 = 53

Since the equation is true, x = 70 is the correct solution.

Example 4

Solve the one-step equation below.

112 = k – 48 

Solution

Notice that this example is slightly different from the previous examples since the variable is on the right-hand side of the equation. Remember that we need to isolate the variable on either side of the equation. We will perform the inverse operation and add 48 from both sides of the equation. Hence, we have,

112 = k – 48  Given
112 + 48 = k – 48 + 48 Add 48 from both sides of the equation
160 = k Simplify

Checking

To check the answer, substitute 160 into the variable k and see if the equation is true:

112 = k – 48 
112 = 160 – 48  
112 = 112

Since the equation is true, k = 160 is the correct solution.

Solving One-Step Equations with Multiplication

A one-step equation involving multiplication has a number ( other than 1 ) in front of the variable. To solve it, we must multiply both sides of this equation by this number.

Examples

Example 1

Solve the one-step equation: 5b = 45.

Solution

In this example, 5b implies 5 times b, which involves multiplication. Since we want to isolate the variable b on the left-hand side of the equation, we will perform the inverse operation and divide both sides of the equation by 5. Hence, we have,

5b = 45 Given

$\frac{5b}{5}$  = $\frac{45}{5}$  Divide both sides of the equation by 5

b = 9 Simplify

Checking

To check the answer, substitute 9 into the variable b and see if the equation is true:

5b = 45
5 × 9 = 45
45 = 45

Since the equation is true, b = 9 is the correct solution.

Example 2

Solve for y in the following equation: 8y = 96.

Solution

In this example, 8y implies 8 times y, which involves multiplication. Since we want to isolate the variable y on the left-hand side of the equation, we will perform the inverse operation and divide both sides of the equation by 8. Thus, we have,

8y = 96 Given

$\frac{8y}{8}$  = $\frac{96}{8}$  Divide both sides of the equation by 8

y = 12 Simplify

Checking

To check the answer, substitute 12 into the variable y and see if the equation is true:

8y = 96
8 × 12 = 96
96 = 96

Since the equation is true, y = 12 is the correct solution.

Example 3

Solve for c: 

7c = 63

Solution

In this example, 7c implies 7 times c, which involves multiplication. Since we want to isolate the variable c on the left-hand side of the equation, we will perform the inverse operation and divide both sides of the equation by 7. Thus, we have,

7c = 63 Given

$\frac{7c}{7}$  = $\frac{63}{7}$  Divide both sides of the equation by 7

c = 9 Simplify

Checking

To check the answer, substitute 9 into the variable c and see if the equation is true:

7c = 63
7 × 9 = 63
63 = 63

Since the equation is true, c = 9 is the correct solution.

Example 4

Solve the one-step equation below.

168 = 12d

Solution

In this example, 12d implies 12 times d, which involves multiplication. Notice that it is slightly different from the previous examples since the variable is on the right-hand side of the equation. Remember that we need to isolate the variable on either side of the equation. We will perform the inverse operation and divide both sides by 12. Thus, we have,

168 = 12d Given

$\frac{168}{12}$ =$\frac{12d}{12}$  Divide both sides of the equation by 12

14 = d Simplify

Checking

To check the answer, substitute 14 into the variable d and see if the equation is true:

168 = 12d 
168 = 12 × 14  
168 = 168

Since the equation is true, d = 14 is the correct solution.

Solving One-Step Equations with Division

A one-step equation with division involves a fraction in which the numerator is a variable, and a denominator is a number. To solve a one-step equation with division, we must multiply both sides by the number in the fraction’s denominator.

What is an example of a two step equation?

What are some examples one step equation has no solution?

What is an example of 1 solution?