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If 3x ≡ 9 (mod 12), what is the value of x?

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Question: If 3x ≡ 9 (mod 12), what is the value of x?

Options:

  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer: 2

Solution: 

Dividing both sides by 3 gives x ≡ 3 (mod 12), which means x can be 3.

If 3x ≡ 9 (mod 12), what is the value of x?

Practice Questions

Q1
If 3x ≡ 9 (mod 12), what is the value of x?
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Questions & Step-by-Step Solutions

If 3x ≡ 9 (mod 12), what is the value of x?
  • Step 1: Start with the equation 3x ≡ 9 (mod 12).
  • Step 2: Understand that 'mod 12' means we are working with numbers that wrap around after 12.
  • Step 3: To simplify the equation, we can divide both sides by 3. This is allowed because 3 has a multiplicative inverse modulo 12.
  • Step 4: Dividing both sides gives us x ≡ 3 (mod 12).
  • Step 5: This means that x can be 3, or any number that is 3 more than a multiple of 12 (like 3, 15, 27, etc.).
  • Step 6: The simplest solution is x = 3.
  • Modular Arithmetic – Understanding how to solve equations in the context of modular arithmetic, including the properties of congruences.
  • Divisibility – Recognizing when it is valid to divide both sides of a congruence by a number, particularly in relation to the modulus.
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