One-step equations

Quick answer

You can solve a one-step equation by using the inverse operation to find the missing number. For example, if x + 5 = 12, you can subtract 5 from both sides to find that x = 7.

Learning outcome

By the end of this page, you will be able to solve one-step equations by using the inverse operation to find the missing number.

• You can add or subtract to find a missing number.
• You can multiply or divide to find a missing number.
• You can check your answer by putting it back into the equation.
• You can use real-life problems to create and solve one-step equations.

Why this matters

One-step equations are the first step into algebra, which is a way of solving puzzles with numbers and letters. You already use this kind of thinking when you play games, share snacks, or work out how many more cookies you need. Understanding one-step equations helps you solve problems in maths, science, and everyday life. In the future, you’ll use these skills to solve bigger puzzles and more complex problems!

How it works

When you see an equation like x + 3 = 7, you are trying to find the value of x. To do this, you must use the inverse operation, which is the opposite of what is happening in the equation.

1. Look at the equation and find what operation is being done to the variable (like x).
2. Do the inverse operation to both sides of the equation to isolate the variable.
3. Check your answer by putting it back into the original equation.

For example:

• If x + 3 = 7, the operation is addition. So, you subtract 3 from both sides.
• If x ÷ 4 = 8, the operation is division. So, you multiply both sides by 4.

Examples you can see

Let’s look at some simple equations and how to solve them step by step.

Example 1: Addition

x + 6 = 10

1. The operation is addition, so we use subtraction to undo it.
2. Subtract 6 from both sides: x + 6 – 6 = 10 – 6
3. This gives us: x = 4
4. Check: 4 + 6 = 10 ✓

Example 2: Subtraction

y – 5 = 12

1. The operation is subtraction, so we use addition to undo it.
2. Add 5 to both sides: y – 5 + 5 = 12 + 5
3. This gives us: y = 17
4. Check: 17 – 5 = 12 ✓

Example 3: Multiplication

3 × z = 15

1. The operation is multiplication, so we use division to undo it.
2. Divide both sides by 3: 3 × z ÷ 3 = 15 ÷ 3
3. This gives us: z = 5
4. Check: 3 × 5 = 15 ✓

Example 4: Division

m ÷ 2 = 9

1. The operation is division, so we use multiplication to undo it.
2. Multiply both sides by 2: m ÷ 2 × 2 = 9 × 2
3. This gives us: m = 18
4. Check: 18 ÷ 2 = 9 ✓

Try it as a mini adventure

Adventure: The Treasure Hunt

You are on a treasure hunt and need to solve clues to find the treasure. Each clue is a one-step equation!

1. Clue 1: x + 4 = 10 – What is x?
2. Clue 2: y – 3 = 7 – What is y?
3. Clue 3: 5 × z = 25 – What is z?
4. Clue 4: m ÷ 6 = 4 – What is m?

Find the answers to all clues and use them to unlock the treasure chest!

Common mistakes

• Mistake: Forgetting to do the same operation to both sides of the equation.
• Why it happens: You might think you can just do it to one side.
• Fix: Always do the same thing to both sides to keep the equation balanced.

• Mistake: Mixing up the inverse operation (using subtraction when you need addition).
• Why it happens: Confusion about what is the opposite of an operation.
• Fix: Remember that addition and subtraction are inverses, and multiplication and division are inverses.

• Mistake: Not checking the answer.
• Why it happens: Rushing through the problem.
• Fix: Always put your answer back into the original equation to check if it works.

Parent and carer guide

Helping your child with one-step equations can be fun and rewarding!

1. Explain the idea: Use simple language like “We are trying to find the missing number.”
2. Use real-life examples: For example, “You had some cookies, ate 3, and now have 7 left. How many did you start with?”
3. Encourage checking: Always double-check the answer by putting it back into the equation.
4. Practice together: Try solving equations using counters, drawings, or a whiteboard.
5. Be patient: It might take a few tries to get it right, and that’s okay!

Remember, the goal is not just to get the answer, but to understand how to find it. Keep it playful and supportive!

Practice questions

1. Solve: x + 8 = 15
2. Solve: y – 6 = 9
3. Solve: 4 × z = 24
4. Solve: m ÷ 5 = 7
5. Solve: a + 12 = 20
6. Solve: b – 4 = 11
7. Solve: 3 × c = 18
8. Solve: d ÷ 3 = 6
9. Solve: e + 10 = 17
10. Solve: f – 8 = 12

Answers

1. x = 7
2. y = 15
3. z = 6
4. m = 35
5. a = 8
6. b = 15
7. c = 6
8. d = 18
9. e = 7
10. f = 20

FAQ

What is a one-step equation?

A one-step equation is an equation that needs only one operation (addition, subtraction, multiplication, or division) to solve for the missing number.

Why do we use inverse operations?

We use inverse operations to undo what was done to the variable so we can find its value. For example, if something was added, we subtract to find the missing number.

Can I solve equations with letters other than x?

Yes! Any letter can be used as a variable. Common ones are y, z, m, and a. The process is the same.

How do I know which inverse operation to use?

If the equation has addition, use subtraction. If it has subtraction, use addition. If it has multiplication, use division. If it has division, use multiplication.

Is it okay to make mistakes?

Absolutely! Making mistakes is part of learning. Each mistake helps you understand better. Keep practicing and you’ll get better!