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If 2x ≡ 4 (mod 6), what is the smallest non-negative integer solution for x?

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Question: If 2x ≡ 4 (mod 6), what is the smallest non-negative integer solution for x?

Options:

  1. 0
  2. 1
  3. 2
  4. 3

Correct Answer: 2

Solution: 

Dividing both sides by 2 gives x ≡ 2 (mod 3), hence the smallest non-negative solution is 2.

If 2x ≡ 4 (mod 6), what is the smallest non-negative integer solution for x?

Practice Questions

Q1
If 2x ≡ 4 (mod 6), what is the smallest non-negative integer solution for x?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If 2x ≡ 4 (mod 6), what is the smallest non-negative integer solution for x?
  • Step 1: Start with the equation 2x ≡ 4 (mod 6).
  • Step 2: Understand that 'mod 6' means we are looking for solutions that are equivalent when divided by 6.
  • Step 3: To simplify the equation, divide both sides by 2. This gives us x ≡ 2 (mod 3).
  • Step 4: Now, we need to find the smallest non-negative integer that satisfies x ≡ 2 (mod 3).
  • Step 5: The smallest non-negative integer that is equivalent to 2 when divided by 3 is simply 2.
  • 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 modular contexts.
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