Solving One-Step Equations

What Is an Equation?

Equation = Balance

An equation is a mathematical statement that shows two expressions are equal. The equals sign (=) acts like the center of a balance scale.

Think of a Balance Scale

x + 5

=

12

Whatever you do to one side, you must do to the other side to keep the scale balanced!

The Goal: Isolate the Variable

To solve an equation, we want to get the variable alone on one side. We do this by using inverse operations - operations that "undo" each other.

Inverse Operations

Operation		Inverse Operation
Addition (+)	↔	Subtraction (-)
Subtraction (-)	↔	Addition (+)
Multiplication (x)	↔	Division (/)
Division (/)	↔	Multiplication (x)

Types of One-Step Equations

Addition Equations

x + 5 = 12

To solve: Subtract the same number from both sides.
x + 5 - 5 = 12 - 5
x = 7

Subtraction Equations

x - 8 = 15

To solve: Add the same number to both sides.
x - 8 + 8 = 15 + 8
x = 23

Multiplication Equations

3x = 21

To solve: Divide both sides by the same number.
3x / 3 = 21 / 3
x = 7

Division Equations

x / 4 = 6

To solve: Multiply both sides by the same number.
(x / 4) x 4 = 6 x 4
x = 24

Pro Tip: Always check your answer! Substitute your solution back into the original equation to verify it works.

Remember: Whatever operation you perform on one side of the equation, you MUST do the same to the other side to keep it balanced.

Steps to Solve One-Step Equations

Identify the operation being performed on the variable
Apply the inverse operation to both sides
Simplify to isolate the variable
Check your answer by substituting back

Worked Examples

Let's work through solving different types of one-step equations step by step.

Example 1: Addition Equation

Solve: x + 7 = 15

1

Identify the operation:
7 is being added to x.

2

Apply the inverse operation:
The inverse of addition is subtraction. Subtract 7 from both sides.
x + 7 - 7 = 15 - 7

3

Simplify:
x = 8

4

Check: Substitute x = 8 into the original equation.
8 + 7 = 15 ✓

Solution: x = 8

Example 2: Subtraction Equation

Solve: n - 12 = 25

1

Identify the operation:
12 is being subtracted from n.

2

Apply the inverse operation:
The inverse of subtraction is addition. Add 12 to both sides.
n - 12 + 12 = 25 + 12

3

Simplify:
n = 37

4

Check: Substitute n = 37 into the original equation.
37 - 12 = 25 ✓

Solution: n = 37

Example 3: Multiplication Equation

Solve: 5y = 40

1

Identify the operation:
y is being multiplied by 5.

2

Apply the inverse operation:
The inverse of multiplication is division. Divide both sides by 5.
5y / 5 = 40 / 5

3

Simplify:
y = 8

4

Check: Substitute y = 8 into the original equation.
5 x 8 = 40 ✓

Solution: y = 8

Example 4: Division Equation

Solve: m / 6 = 9

1

Identify the operation:
m is being divided by 6.

2

Apply the inverse operation:
The inverse of division is multiplication. Multiply both sides by 6.
(m / 6) x 6 = 9 x 6

3

Simplify:
m = 54

4

Check: Substitute m = 54 into the original equation.
54 / 6 = 9 ✓

Solution: m = 54

Example 5: Real-World Problem

Sarah earned $45 this week. This is $18 more than she earned last week. How much did she earn last week?

1

Write the equation:
Let x = amount earned last week
x + 18 = 45

2

Apply the inverse operation:
Subtract 18 from both sides.
x + 18 - 18 = 45 - 18

3

Simplify:
x = 27

4

Check: Does 27 + 18 = 45?
Yes! 27 + 18 = 45 ✓

Sarah earned $27 last week.

Practice Problems

Solve each equation by applying inverse operations.

Problem 1

x + 9 = 20

Problem 2

y - 14 = 32

Problem 3

7n = 56

Problem 4

m / 5 = 12

Problem 5

k + 35 = 100

Check Your Understanding: Equation Solver Challenge

Test your equation-solving skills with this 6-question challenge!

Equation Solver Challenge

Score: 0 / 6

Question 1 of 6

Challenge Complete!

0/6

Next Steps

Key Takeaways:

An equation shows that two expressions are equal
Use inverse operations to isolate the variable
Addition and subtraction are inverse operations
Multiplication and division are inverse operations
Always do the same operation to both sides of the equation
Check your answer by substituting back into the original equation

Practice identifying the operation in different equations
Try creating and solving your own word problems
You have completed the Expressions & Equations unit!