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Equations with one solution, no solution or infinitely many

8th grade (Year 9 in England) · 16 questions · Common Core: 8.EE.C.7.A · England: KS3 Algebra

Name

Date

Score/ 16

  1. Question 1

    7x − 3 = □x + 0. For which value of □ does the equation have NO solution?

    Answer

  2. Question 2

    How many solutions does 3(x + 5) = 3x + 15 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

  3. Question 3

    8x − 6 = 8x + □. Which number in the box gives infinitely many solutions?

    Answer

  4. Question 4

    How many solutions does 4(x + 6) = 4x + 20 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

  5. Question 5

    3x − 7 = □x + (−5). For which value of □ does the equation have NO solution?

    Answer

  6. Question 6

    How many solutions does 3(x + 4) = 3x + 12 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

  7. Question 7

    2x = □x + 7. For which value of □ does the equation have NO solution?

    Answer

  8. Question 8

    How many solutions does 3(x + 6) = 3x + 18 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

  9. Question 9

    2x + 2 = 2x + □. Which number in the box gives infinitely many solutions?

    Answer

  10. Question 10

    How many solutions does 4(x + 1) = 4x + 9 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

  11. Question 11

    2x + 9 = □x + 14. For which value of □ does the equation have NO solution?

    Answer

  12. Question 12

    How many solutions does 3(x + 1) = 3x + 3 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

  13. Question 13

    6x − 8 = □x + (−6). For which value of □ does the equation have NO solution?

    Answer

  14. Question 14

    How many solutions does 4(x + 1) = 4x + 8 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

  15. Question 15

    9x − 2 = 9x + □. Which number in the box gives infinitely many solutions?

    Answer

  16. Question 16

    How many solutions does 5(x + 2) = 5x + 15 have?

    • A. No solution
    • B. Infinitely many solutions
    • C. Exactly one solution

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Answer key: Equations with one solution, no solution or infinitely many

  1. 1. 7

  2. 2. B. Infinitely many solutions

  3. 3. -6

  4. 4. A. No solution

  5. 5. 3

  6. 6. B. Infinitely many solutions

  7. 7. 2

  8. 8. B. Infinitely many solutions

  9. 9. 2

  10. 10. A. No solution

  11. 11. 2

  12. 12. B. Infinitely many solutions

  13. 13. 6

  14. 14. A. No solution

  15. 15. -2

  16. 16. A. No solution