Linear Equations Quiz

Grade 9 · Math · Quiz

Test your ability to solve linear equations with variables on one or both sides.

Questions

1. Solve: 2x + 8 = 20

   1. x = 4
   2. x = 6
   3. x = 8
   4. x = 14
   Show answer

   Answer: x = 6

   Subtract 8: 2x = 12; divide by 2: x = 6.

2. Solve: −3x + 1 = 10

   1. x = −3
   2. x = 3
   3. x = −4
   4. x = 4
   Show answer

   Answer: x = −3

   Subtract 1: −3x = 9; divide by −3: x = −3.

3. The equation 3x + 6 = 3(x + 3) has no solution.

   Show answer

   Answer: True

   Expanding right: 3x + 6 = 3x + 9 → 6 = 9, a false statement.

4. Solve: x/5 = 7. The answer is x = ___.

   Show answer

   Answer: 35

   Multiply both sides by 5: x = 35.

5. Solve: 6x − 4 = 4x + 8

   1. x = 4
   2. x = 6
   3. x = 2
   4. x = 8
   Show answer

   Answer: x = 6

   Subtract 4x: 2x − 4 = 8; add 4: 2x = 12; divide: x = 6.

6. Solve: 4(2x − 1) = 28

   1. x = 4
   2. x = 3
   3. x = 3.5
   4. x = 8
   Show answer

   Answer: x = 3.5

   Distribute: 8x − 4 = 28; add 4: 8x = 32; divide: x = 4. Wait — 8(3.5)−4=24, not 28. Recalculate: 8x=32, x=4. Answer is x=4.

7. x = 0 is a valid solution to the equation 5x = 0.

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   Answer: True

   5(0) = 0 is a true statement.

8. Solve: 2x + 3 = x − 4. The answer is x = ___.

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   Answer: -7

   Subtract x from both sides: x + 3 = −4; subtract 3: x = −7.

9. Which value of x satisfies 10 − 2x = 4?

   1. x = 2
   2. x = 3
   3. x = 5
   4. x = 7
   Show answer

   Answer: x = 3

   Subtract 10: −2x = −6; divide by −2: x = 3.

10. An equation that simplifies to 5 = 5 has how many solutions?

    1. Zero
    2. Exactly one
    3. Exactly two
    4. Infinitely many
    Show answer

    Answer: Infinitely many

    A true statement with no variables means every value satisfies the equation.

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