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Grade 6–8Common Core (CCSS) · Math: algebra

Equation Worksheets — Solve for x with Answer Key

Create equation worksheets in seconds, from one-step equations to x on both sides, with real-life word problems and a complete answer key.

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Equations · 12-14 years

Name: ____________________

Worked example

  1. The goal: get x alone on one side. Do the same thing on both sides of the equals sign.
  2. Example: x + 5 = 12. Subtract 5 from both sides: x = 12 − 5.
  3. Answer: x = 7. Check: 7 + 5 = 12. ✓
Example: how to solve it
1.

Solve: 4x + 3 = 23

2.

Noa thinks of a number, multiplies it by 7 and adds 27. The result is 90. What is the number?

3.

Solve: 7x + 2 = 16

4.

6 equally priced tickets and a 13 kr programme cost 55 kr in total. What does one ticket cost? Answer with the correct unit.

5.

Solve: 6x + 12 = 48

6.

Sara thinks of a number, multiplies it by 4 and adds 10. The result is 22. What is the number?

7.

Solve: 3x + 21 = 39

8.

A gym charges 24 kr per month plus 2 kr per visit. Amira paid 38 kr. How many visits was that? Answer with the correct unit.

9.

Solve: 4x + 5 = 13

10.

Nour thinks of a number, multiplies it by 6 and adds 20. The result is 62. What is the number?

11.

Solve: 7x + 25 = 67

12.

A rectangle is 10 cm longer than it is wide. Its perimeter is 84 cm. How wide is it? Answer with the correct unit.

13.

Solve: 5x + 17 = 42

14.

9 equally priced tickets and a 28 kr programme cost 154 kr in total. What does one ticket cost? Answer with the correct unit.

15.

Solve: 8x + 25 = 49

16.

A taxi costs 2 kr to start plus 2 kr per km. A trip costs 14 kr. How many km was the trip? Answer with the correct unit.

17.

Solve: 8x + 6 = 38

18.

Vera thinks of a number, multiplies it by 4 and adds 28. The result is 56. What is the number?

19.

Solve: 3x + 6 = 39

20.

2 equally priced tickets and a 23 kr programme cost 41 kr in total. What does one ticket cost? Answer with the correct unit.

Answer key

  1. 1. x = 5
  2. 2. 9
  3. 3. x = 2
  4. 4. 7 kr
  5. 5. x = 6
  6. 6. 3
  7. 7. x = 6
  8. 8. 7 visits
  9. 9. x = 2
  10. 10. 7
  11. 11. x = 6
  12. 12. 16 cm
  13. 13. x = 5
  14. 14. 14 kr
  15. 15. x = 3
  16. 16. 6 km
  17. 17. x = 4
  18. 18. 7
  19. 19. x = 11
  20. 20. 9 kr

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Topics on this worksheet

Areas on this sheet

  • Algebra · 20

Step 1 of 5

Choose an area

Your choices

Area
Algebra
Exercise type
Equations
Age
12–14 years
Difficulty
Easy
Number of tasks
20
Task format
Mixed
Paper size
US Letter
1. Choose content
Area
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How to use the tool

  1. The exercise type Equations is already selected.
  2. Choose age and difficulty: easy gives one-step equations, hard gives x on both sides.
  3. Choose calculations, word problems or mixed, then print or save as PDF.

About this generator

Solving equations is the heart of early algebra. This generator lets pupils practise the balance method with equations that always have a whole-number answer. At the easy level the tasks are one-step equations such as x + 7 = 15. At the medium level they become two-step equations like 3x + 5 = 26, where pupils first subtract and then divide. At the hard level x appears on both sides, for example 7x + 4 = 3x + 24, and negative solutions are included. Word problems turn equations into everyday situations: a taxi fare with a starting fee, a gym membership, a plumber’s bill, rows of chairs in a hall or a rectangle with a known perimeter. The answer key shows the solution with its unit, such as km, hours, chairs or the local currency, so pupils can check that their answer makes sense. Every equation is generated and checked by the website, and a new version gives new numbers instantly.

Popular uses

  • Introducing the balance method
  • Practising two-step equations
  • Word problems that need an equation
  • Revision before an algebra test

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Frequently asked questions

How do I pick the right level?
Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
Can I see the problems before printing?
Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
How do I include an answer key?
Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
What does the question mark next to a problem do?
It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
How do you solve a two-step equation?
Undo addition or subtraction first, then undo multiplication or division. For 3x + 5 = 26: subtract 5 to get 3x = 21, then divide by 3 to get x = 7.
Do all equations have whole-number solutions?
Yes. The numbers are chosen so that every solution is an integer, which keeps the focus on the method.
Do the equation word problems have units?
Yes, answers show units such as km, h, cm or chairs where the situation needs them.

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