For class, tutoring, or a quick practice at home

One-step equations worksheet generator

Solve one-step addition and multiplication equations using an inverse operation. Each generated equation has an integer solution; substitute it into the original equation to check it.

Free to use · no sign-up · adjustable difficulty · print or save as PDF · separate answer key

Mixed worksheet modules

Select one or more modules and set the question count for each. Leave all unchecked to use the page topic.

Advanced arithmetic settings
Operators
Print fields and style
View worksheet

For a clean printout, turn off “Headers and footers” in the print dialog. One-click PDF never includes the date, page title, or web address.

This worksheet is made on your device. We do not ask for student details.

Name: ____________________Date: ____________________
1.x + 1 = 24
2.x + 12 = 24
3.x + 3 = 32
4.3x = 87
5.6x = 42
6.x + 28 = 58
7.x + 28 = 44
8.x + 4 = 13
9.2x = 8
10.5x = 20
11.x + 1 = 10
12.6x = 6
13.x + 29 = 30
14.x + 29 = 48
15.x + 12 = 20
16.x + 9 = 14
17.5x = 115
18.x + 29 = 47
19.5x = 55
20.x + 21 = 32
Answer key
1. x = 23
2. x = 12
3. x = 29
4. x = 29
5. x = 7
6. x = 30
7. x = 16
8. x = 9
9. x = 4
10. x = 4
11. x = 9
12. x = 1
13. x = 1
14. x = 19
15. x = 8
16. x = 5
17. x = 23
18. x = 18
19. x = 11
20. x = 11
Advertisement
02

What this worksheet practises

  • Identify the operation applied to the unknown
  • Use an inverse operation on both sides
  • Substitute the solution to verify it

What appears on the sheet

  • Easy uses addition equations x + b = c with values from 1 to 10.
  • Medium and hard mix addition equations with multiplication equations ax = c; coefficients are 2 to 6 for medium and 2 to 12 for hard.
  • Every equation has a positive integer solution and requires one inverse operation.

Make a sheet in three steps

Choose the level and question count, generate the sheet, then print or download it. Keep the seed if you want exactly the same questions again.

Algorithms

Choose a method for this problem type

CategoryAlgebra · equations
Problem patternOne-step addition equation
Worked examplex + 17 = 42, so x = 25

How to recognize it

  • An unknown and a constant are joined by one operation.
  • Both sides of the equals sign represent the same value.
x + 1742−17 both sides
A balanced scale with x plus 17 on one side and 42 on the other; 17 is removed from both sides.
01
Visual model

Balance model

Best for: Understanding why the same change is made on both sides

Keep equality balanced while removing 17 from both sides.

  1. Represent both sides as equal weights.
  2. Remove 17 from the left and the right.
  3. The remaining balance shows x = 25.

Trade-off: Explains equality well; more complex equations need increasingly abstract models.

02
Written algorithm

Inverse operation

Best for: A concise general solution

Undo addition with subtraction while preserving equality.

  1. Subtract 17 from both sides.
  2. x + 17 − 17 = 42 − 17.
  3. Simplify to x = 25.

Trade-off: Efficient and scalable; writing the operation on both sides prevents unexplained “moving.”

03
Mental strategy

Think of the missing addend

Best for: Simple values and checking

Ask what must be added to 17 to make 42.

  1. Count from 17 to 20: 3.
  2. Count from 20 to 40: 20.
  3. Count to 42: 2; total 25.

Trade-off: Intuitive for addition equations, but it does not replace a general algebra method.

Check the resultSubstitute the result: 25 + 17 = 42.

Standards

Grade and standards reference

These mappings are planning references, not certification of curriculum alignment.

One-step equationsGrades 6CCSS 6.EE
Advertisement
03

Teaching notes

  • Encourage one transformation per written line.
  • Always finish by substituting the answer into the original equation.
04

Questions teachers and parents ask

What is a one-step equation?

A one-step equation is solved with a single inverse operation, such as x + 17 = 42 (subtract 17 from both sides) or 3x = 21 (divide both sides by 3). It is the standard first step into algebra.

Can solutions be negative?

No. The generated equations use positive integer solutions. The difficulty level changes the range of those values.

Why write the check?

Substitution confirms the value works and reinforces the meaning of equality.

05

Teach the idea, then practise it

Learning goals

  • Interpret the equals sign as a balance, not a signal to calculate.
  • Use inverse operations while preserving equality.
  • Verify a solution through substitution into the original equation.

Quick understanding checks

  • Every written transformation preserves equality.
  • Substitution makes the original left and right sides equal.

Suggested teaching progression

  1. BalanceExplore missing-number statements and equivalent expressions.
  2. StructureIdentify what operation has been applied to the unknown.
  3. Solve and verifyUndo the operation, then substitute the result into the original equation.

Common misconceptions and responses

The equals sign is read as “the answer comes next.”

Use true and false number sentences with expressions on both sides to establish equivalence.

An operation is changed on only one side of the equation.

Model a balance and write the same transformation on both sides on each line.

06

Curriculum and teaching references

These external sources provide curriculum context or evidence-informed teaching guidance. They do not endorse this generator, and local curriculum requirements should take priority.

Content reviewExplanations and examples reviewed 9 October 2026. Found a problem? Send a correction

07

Focused worksheet sets

One-step equations practice with answersCreate 20 printable introductory equations with integer solutions and a separate answer key.
08

More worksheet makers

Addition worksheet generatorMental addition or written addition with carrying.Subtraction worksheet generatorSubtraction with a choice of borrowing rules.Multiplication worksheet generatorMultiplication facts or multi-digit calculation.Division worksheet generatorExact division or division with remainders.Mixed arithmetic worksheet generatorSingle-step addition, subtraction, multiplication and division on one sheet.Fractions worksheet generatorProper-fraction addition with like or unlike denominators.Area and perimeter worksheet generatorLabelled diagrams for area, perimeter and missing sides.Unit conversion worksheet generatorLength, mass, volume and area conversions.
Advertisement