One Step Equations Worksheet With Answers: How to Solve & Practice

A one step equation is an equation that can be solved in a single operation, such as x + 5 = 12 or 3x = 18. To solve it, you apply the inverse operation to both sides, isolating the variable to find its value. A one step equations worksheet with answers gives students problems to solve plus the worked solutions, so they can check their reasoning immediately instead of waiting for a teacher to grade it. This guide covers how these equations work, how to solve each type, a ready-to-use practice set with answers, and the mistakes worth watching for.

What Are One Step Equations

A one step equation is an algebraic statement where the variable appears only once and is connected to a number by exactly one operation — addition, subtraction, multiplication, or division. There is no exponent on the variable, no variable on both sides, and no parentheses to distribute. That single-operation structure is what makes these the first real algebra problems most students meet.

The standard form looks like one of these four patterns:

• x + a = b (addition)
• x − a = b (subtraction)
• ax = b (multiplication, where a is the coefficient)
• x/a = b (division)

Two vocabulary terms matter here. The variable is the unknown letter, usually x, representing the value you’re solving for. The coefficient is the number multiplying a variable, so in 4x = 20 the coefficient is 4. Recognizing which of the four patterns you’re looking at is most of the battle — once you name the operation, you know exactly what to undo.

Conceptually, an equation is a balanced scale. Whatever sits on the left equals whatever sits on the right, and any change you make must be applied to both sides to keep that balance true. This balance idea is the foundation of all equation solving, and it’s a core idea in early algebra curricula emphasized by Illustrative Mathematics.

How to Solve One Step Equations

Use the inverse operation — the opposite operation — to cancel whatever is attached to the variable. Addition undoes subtraction, subtraction undoes addition, multiplication undoes division, and division undoes multiplication. Whatever you do to one side, do to the other.

The four operation types

Addition: x + 7 = 15. The variable has 7 added to it, so subtract 7 from both sides. x + 7 − 7 = 15 − 7, giving x = 8.

Subtraction: x − 4 = 9. The variable has 4 subtracted, so add 4 to both sides. x − 4 + 4 = 9 + 4, giving x = 13.

Multiplication: 6x = 42. The variable is multiplied by 6, so divide both sides by 6. 6x ÷ 6 = 42 ÷ 6, giving x = 7.

Division: x/5 = 3. The variable is divided by 5, so multiply both sides by 5. (x/5) × 5 = 3 × 5, giving x = 15.

Always verify your answer

Substitute your solution back into the original equation. For x + 7 = 15 with x = 8: 8 + 7 = 15, which is true. For 6x = 42 with x = 7: 6 × 7 = 42, true. Checking takes seconds and catches nearly every careless error, which is why it’s a habit worth building from the start. Khan Academy’s algebra materials walk through this same inverse-operations reasoning step by step at Khan Academy.

One Step Equations Worksheet With Answers

Work through each problem first, then check the answer and reasoning below it. The set is organized by operation so you can drill one skill at a time.

Addition equations

1. x + 9 = 20 → x = 11 (subtract 9 from both sides)
2. x + 13 = 25 → x = 12 (subtract 13)
3. x + 6 = 6 → x = 0 (subtract 6)

Subtraction equations

4. x − 8 = 5 → x = 13 (add 8)
5. x − 14 = 3 → x = 17 (add 14)
6. x − 2 = 0 → x = 2 (add 2)

Multiplication equations

7. 4x = 28 → x = 7 (divide by 4)
8. 9x = 63 → x = 7 (divide by 9)
9. 5x = 0 → x = 0 (divide by 5)

Division equations

10. x/3 = 7 → x = 21 (multiply by 3)
11. x/6 = 4 → x = 24 (multiply by 6)
12. x/8 = 1 → x = 8 (multiply by 8)

Mixed practice

13. x + 15 = 32 → x = 17
14. x − 11 = 19 → x = 30
15. 7x = 56 → x = 8
16. x/9 = 5 → x = 45

One worked example in full: for problem 8, 9x = 63, the coefficient is 9 and it’s multiplying the variable, so divide both sides by 9. 9x ÷ 9 = x, and 63 ÷ 9 = 7, so x = 7. Check: 9 × 7 = 63. Correct.

For a self-check, remember the pattern: if the equation involves addition or subtraction, your answer is a single number you can verify by substitution. If it involves multiplication or division, divide or multiply to undo it. The National Council of Teachers of Mathematics notes that fluency with inverse relationships is a key building block for later equation work.

Common Mistakes and Practice Tips

Most errors in this topic are predictable, which makes them easy to fix once you know what to look for.

• Applying the wrong inverse operation. If the problem shows subtraction, some students add the wrong amount or subtract again. Name the operation before you act on it: “This is addition, so I subtract.”
• Changing only one side. Equations stay balanced only if you do the same thing to both sides. Writing x + 7 = 15 → x = 15 is a balance error.
• Sign handling. In x + (−4) = 10, the inverse of adding −4 is adding +4, so x = 14. Watch negative numbers carefully and keep them attached to their sign.
• Dividing when you should multiply. For x/4 = 8, the variable is divided by 4, so multiply by 4 to get x = 32, not divide for x = 2.
• Skipping the check. Substituting takes a few seconds and confirms the answer.

For building speed, try timed rounds of ten problems, then review only the ones you missed. Mix operations frequently rather than staying on one type, since switching between inverse operations is where real fluency develops. Keep a short error log with the problem, the mistake, and the correction — patterns show up fast and give you a focused target for the next practice session.

Key Takeaways

• A one step equation is solved with a single inverse operation, applied to both sides to keep the equation balanced.
• Addition is undone by subtraction, subtraction by addition, multiplication by division, and division by multiplication.
• Always substitute your answer back into the original equation to verify it.
• Worksheets with answers let you self-check immediately, which speeds up learning more than waiting for outside feedback.
• Most mistakes come from wrong inverse operations, changing only one side, or mishandling signs — naming the operation before solving prevents all three.