Step 2: Notice that both 8 and 4 can be divided by 4. So, divide the entire equation by 4.
Step 3: After dividing, the equation becomes 2x ≡ 1 (mod 3).
Step 4: Now, we need to find the value of x that satisfies 2x ≡ 1 (mod 3).
Step 5: To solve for x, we can test values for x: If x = 0, 2(0) = 0 (not 1); If x = 1, 2(1) = 2 (not 1); If x = 2, 2(2) = 4, and 4 mod 3 = 1 (this works).
Step 6: Therefore, the solution is x = 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.
