How to Solve Two-Step Equations

What You Will Learn

• Recognise the operations in a two-step equation.
• Use inverse operations in the correct order.
• Solve equations involving addition, subtraction, multiplication and division.
• Check a solution by substituting it into the original equation.
• Write and solve a simple equation from a word problem.

1. What Is an Equation?

An equation is a mathematical statement that says two expressions have the same value. The equals sign (=) means that the left side and right side are balanced.

A two-step equation needs two operations to isolate the unknown. For example, 3x + 5 = 20 includes multiplication by 3 and addition of 5.

2. Understand Inverse Operations

Inverse operations undo one another. Use them to isolate the variable while keeping the equation balanced.

3. Solve an Equation with Addition and Multiplication

Worked example: Solve 3x + 5 = 20

Work backwards from the operations around the variable. Undo addition first, then undo multiplication.

4. Solve an Equation with Subtraction and Multiplication

Worked example: Solve 4x − 7 = 13

1. Add 7 to both sides to undo subtracting 7: 4x = 20.
2. Divide both sides by 4: x = 5.
3. Check: 4(5) − 7 = 20 − 7 = 13.

Answer: x = 5. Notice that addition is used first because it reverses the subtraction outside the term 4x.

5. Solve an Equation with Division

Worked example: Solve x/3 + 4 = 9

1. Subtract 4 from both sides: x/3 = 5.
2. Multiply both sides by 3: x = 15.
3. Check: 15/3 + 4 = 5 + 4 = 9.

Answer: x = 15.

6. When Brackets Are Included

Some equations show a multiplication outside brackets. First simplify the bracket expression or use the distributive property, depending on the method you have learned.

Worked example: Solve 2(x + 3) = 18

1. Divide both sides by 2: x + 3 = 9.
2. Subtract 3 from both sides: x = 6.
3. Check: 2(6 + 3) = 2 × 9 = 18.

Answer: x = 6.

7. Equations with Negative Numbers

Worked example: Solve 5 − 2x = −3

1. Subtract 5 from both sides: −2x = −8.
2. Divide both sides by −2: x = 4.
3. Check: 5 − 2(4) = 5 − 8 = −3.

Answer: x = 4. Remember that a negative divided by a negative gives a positive result.

8. Turn a Word Problem into an Equation

Example: A number is multiplied by 4, then 6 is added. The result is 30. Find the number.

1. Let the unknown number be x.
2. “Multiplied by 4” means 4x. “Then 6 is added” means + 6.
3. Write the equation: 4x + 6 = 30.
4. Subtract 6: 4x = 24.
5. Divide by 4: x = 6.

9. A Reliable Method

1. Simplify first if the equation contains brackets or like terms you already know how to combine.
2. Undo addition or subtraction around the variable.
3. Undo multiplication or division to isolate the variable.
4. Check your result in the original equation.

Think of solving as reversing the order of operations. Undo the outside operation first, then continue until the variable is alone.

10. Common Mistakes to Avoid

11. Practice Exercises

Try each problem on paper before opening the answers.

1. Solve: 2x + 3 = 15.
2. Solve: 5x − 4 = 21.
3. Solve: x/4 + 2 = 8.
4. Solve: 3x + 8 = 2.
5. Solve: 7 − 2x = −5.
6. Solve: 3(x + 2) = 24.
7. A number is multiplied by 5 and then 9 is subtracted. The result is 26. Find the number.
8. A taxi charges a fixed fee of $4 plus $2 per kilometre. The total fare is $18. How many kilometres were travelled?

12. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

13. Free Printable Worksheet

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

14. Lesson Summary

• An equation stays balanced when the same operation is applied to both sides.
• Use inverse operations to isolate the variable.
• Undo addition or subtraction before multiplication or division in a typical two-step equation.
• Keep negative signs attached to their numbers.
• Check the final value in the original equation.

Continue Learning

• Grade 6: Solving One-Step Equations
• Grade 6: Algebraic Expressions
• Grade 7: Simplifying Algebraic Expressions
• Grade 7 Maths Learning Path