Equations with Special Solutions Worksheets
Distinguish equations with no solution from identities true for every real number.
Before you begin
Use signed arithmetic, substitute values and read expressions with variables.
Worked example
Solve 6(x + 7) = 6x + 42. State whether there are no solutions or infinitely many solutions.
- Expand the left side to 6x + 42.
- Subtract the x-terms from both sides.
- The remaining equality is true for every x.
Answer: Infinitely many solutions (all real x).
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Solve 4(x + 4) = 4x + 16. State whether there are no solutions or infinitely many solutions.
2
Solve 7(x + 7) = 7x + 50. State whether there are no solutions or infinitely many solutions.
3
Solve 2(x + 4) = 2x + 8. State whether there are no solutions or infinitely many solutions.
4
Solve 10(x + 6) = 10x + 61. State whether there are no solutions or infinitely many solutions.
5
Solve 2(x + 6) = 2x + 12. State whether there are no solutions or infinitely many solutions.
6
Solve 4(x + 4) = 4x + 17. State whether there are no solutions or infinitely many solutions.
Answer Key
1. Infinitely many solutions (all real x).2. No solution.3. Infinitely many solutions (all real x).4. No solution.5. Infinitely many solutions (all real x).6. No solution.