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

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.