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How many solutions does the equation have?

Grade 8 math · Fieldbook Learning

Name ______________________ Date __________

Simplify both sides. If the x terms are the same and the numbers match, every x works (infinite). If the numbers differ, no x works (none). Otherwise there is one solution.

  1. How many solutions does the equation −3x + 9 = −3x + 9 have? Write one, none or infinite.
  2. How many solutions does the equation −2x + 6 = −2x + 10 have? Write one, none or infinite.
  3. How many solutions does the equation −x − 7 = 6x − 9 have? Write one, none or infinite.
  4. How many solutions does the equation x − 3 = −4x + 2 have? Write one, none or infinite.
  5. How many solutions does the equation 8x + 9 = 8x + 7 have? Write one, none or infinite.
  6. How many solutions does the equation −2x − 7 = −2x − 7 have? Write one, none or infinite.
  7. How many solutions does the equation 5x − 4 = 5x − 4 have? Write one, none or infinite.
  8. How many solutions does the equation 5x − 5 = 5x − 5 have? Write one, none or infinite.
  9. How many solutions does the equation −7x + 9 = 5x + 8 have? Write one, none or infinite.
  10. How many solutions does the equation 6x − 17 = 2x − 17 have? Write one, none or infinite.
  11. How many solutions does the equation −2x − 15 = −2x − 13 have? Write one, none or infinite.
  12. How many solutions does the equation 9x + 18 = 9x + 18 have? Write one, none or infinite.
  13. How many solutions does the equation −2x − 8 = −2x − 8 have? Write one, none or infinite.
  14. How many solutions does the equation 7x + 24 = −8x − 7 have? Write one, none or infinite.
  15. How many solutions does the equation 2x + 6 = 2x + 10 have? Write one, none or infinite.
  16. How many solutions does the equation 9x + 3 = −2x + 7 have? Write one, none or infinite.
  17. How many solutions does the equation 14x + 42 = −15x + 41 have? Write one, none or infinite.
  18. How many solutions does the equation 9x + 24 = 9x + 24 have? Write one, none or infinite.
  19. How many solutions does the equation 12x + 37 = 12x + 37 have? Write one, none or infinite.
  20. How many solutions does the equation −12x − 28 = −12x − 33 have? Write one, none or infinite.
More free practice: fieldbooklearning.com/ca/practice/grade-8/how-many-solutions-does-the-equation-have/

Answer key: How many solutions does the equation have?

  1. infinite
  2. none
  3. one
  4. one
  5. none
  6. infinite
  7. infinite
  8. infinite
  9. one
  10. one
  11. none
  12. infinite
  13. infinite
  14. one
  15. none
  16. one
  17. one
  18. infinite
  19. infinite
  20. none