GRADE 6 · MATHEMATICS

Solving One-Step Equations

An equation says that two expressions have the same value. Solving an equation means finding the value of the unknown variable. Learn how to use inverse operations to solve simple equations and check each answer by substituting it back.

Learning time: approximately 25–30 minutes · Beginner level

What You Will Learn

Understand what an equation and solution mean.
Use inverse operations to solve one-step equations.
Solve equations involving addition and subtraction.
Solve equations involving multiplication and division.
Check a solution by substituting it into the original equation.

1. What Is an Equation?

An equation is a mathematical statement that two expressions are equal. The equals sign (=) shows that both sides have the same value.

x + 4 = 10

The letter x is the unknown number. Solving the equation means finding the number that makes the statement true.

For this example, x = 6 because 6 + 4 = 10.

2. Understand Inverse Operations

Inverse operations undo each other.

Operation	Inverse operation	Example
Addition (+)	Subtraction (−)	+ 5 is undone by − 5
Subtraction (−)	Addition (+)	− 3 is undone by + 3
Multiplication (×)	Division (÷)	× 4 is undone by ÷ 4
Division (÷)	Multiplication (×)	÷ 6 is undone by × 6

Balance rule: Whatever you do to one side of an equation, you must do to the other side to keep the equation balanced.

3. Solve Equations with Addition

Use subtraction to undo addition.

Worked example: x + 7 = 15

Subtract 7 from both sides: x + 7 − 7 = 15 − 7.
Simplify: x = 8.
Check: 8 + 7 = 15, which is true.

Solution: x = 8.

4. Solve Equations with Subtraction

Use addition to undo subtraction.

Worked example: y − 5 = 9

Add 5 to both sides: y − 5 + 5 = 9 + 5.
Simplify: y = 14.
Check: 14 − 5 = 9.

Solution: y = 14.

5. Solve Equations with Multiplication

Use division to undo multiplication.

Worked example: 4a = 28

Divide both sides by 4: 4a ÷ 4 = 28 ÷ 4.
Simplify: a = 7.
Check: 4 × 7 = 28.

Solution: a = 7.

6. Solve Equations with Division

Use multiplication to undo division.

Worked example: m ÷ 3 = 6

Multiply both sides by 3: (m ÷ 3) × 3 = 6 × 3.
Simplify: m = 18.
Check: 18 ÷ 3 = 6.

Solution: m = 18.

7. Check Every Solution

Substitute the value you found into the original equation. If both sides have the same value, the solution is correct.

Example: Solve x − 4 = 11. Add 4 to both sides: x = 15. Check by substituting: 15 − 4 = 11. Both sides match, so x = 15 is correct.

8. Solve Simple Word Problems

Example 1: Finding a number

A number plus 9 equals 20. What is the number?

Let the number be x. Write x + 9 = 20. Subtract 9 from both sides: x = 11.

Example 2: Equal groups

Four identical boxes contain 32 pencils altogether. How many pencils are in each box?

Let p be the number in each box. 4p = 32. Divide by 4: p = 8 pencils.

9. Common Mistakes to Avoid

Changing only one side: Do the same operation to both sides of an equation.

Using the same operation instead of its inverse: To undo addition, subtract. To undo multiplication, divide.

Skipping the check: Substitute your answer into the original equation to see if it works.

Forgetting multiplication notation: 4a means 4 multiplied by a.

10. Practice Exercises

Try these before revealing the answers.

x + 6 = 14
y − 8 = 5
3a = 21
m ÷ 4 = 7
p + 12 = 19
5n = 45
A number divided by 6 equals 4. Find the number.
Seven identical bags contain 56 marbles altogether. How many marbles are in each bag?

Show practice answers and working

x = 14 − 6 = 8.
y = 5 + 8 = 13.
a = 21 ÷ 3 = 7.
m = 7 × 4 = 28.
p = 19 − 12 = 7.
n = 45 ÷ 5 = 9.
n ÷ 6 = 4, so n = 4 × 6 = 24.
56 ÷ 7 = 8 marbles per bag.

12. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics