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If 3x ≡ 9 (mod 6), what is the value of x?

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Question: If 3x ≡ 9 (mod 6), what is the value of x?

Options:

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Correct Answer: 2

Solution: 

3x = 9 mod 6 simplifies to x = 3 mod 2, so x = 2.

If 3x ≡ 9 (mod 6), what is the value of x?

Practice Questions

Q1
If 3x ≡ 9 (mod 6), what is the value of x?
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Questions & Step-by-Step Solutions

If 3x ≡ 9 (mod 6), what is the value of x?
  • Step 1: Start with the equation 3x ≡ 9 (mod 6). This means that when you divide 3x and 9 by 6, they leave the same remainder.
  • Step 2: Simplify the right side of the equation. Calculate 9 mod 6. When you divide 9 by 6, the remainder is 3. So, 9 mod 6 = 3.
  • Step 3: Now rewrite the equation: 3x ≡ 3 (mod 6).
  • Step 4: To solve for x, divide both sides of the equation by 3. This gives us x ≡ 1 (mod 2).
  • Step 5: The equation x ≡ 1 (mod 2) means that x can be any number that gives a remainder of 1 when divided by 2.
  • Step 6: The smallest positive solution for x is 1, but we can also express it as x = 1 + 2k, where k is any integer.
  • Step 7: Since the question asks for a specific value, we can choose x = 1 as a valid solution.
  • Modular Arithmetic – Understanding how to solve equations involving congruences and the properties of modular arithmetic.
  • Simplification of Congruences – The ability to simplify equations in modular arithmetic to find solutions.
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