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If 4x ≡ 8 (mod 12), what is the smallest non-negative solution for x?

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Question: If 4x ≡ 8 (mod 12), what is the smallest non-negative solution for x?

Options:

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  2. 1
  3. 2
  4. 3

Correct Answer: 2

Solution: 

Dividing the equation by 4 gives x ≡ 2 (mod 3). The smallest non-negative solution is x = 2.

If 4x ≡ 8 (mod 12), what is the smallest non-negative solution for x?

Practice Questions

Q1
If 4x ≡ 8 (mod 12), what is the smallest non-negative solution for x?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If 4x ≡ 8 (mod 12), what is the smallest non-negative solution for x?
  • Step 1: Start with the equation 4x ≡ 8 (mod 12).
  • Step 2: To simplify the equation, divide both sides by 4. This gives us x ≡ 2 (mod 3).
  • Step 3: The equation x ≡ 2 (mod 3) means that x can be 2, 5, 8, etc., but we want the smallest non-negative solution.
  • Step 4: The smallest non-negative solution for x is 2.
  • Modular Arithmetic – Understanding how to solve equations in the context of modular arithmetic, including the properties of congruences.
  • Divisibility – Recognizing when and how to divide both sides of a congruence by a number, particularly when that number is a divisor of the modulus.
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