This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Interpret the notation. The term "finite 7" in this context typically refers to operations within the ring of integers modulo 7, denoted as Z_7. This means all calculations are performed, and results are expressed, as remainders when divided by 7. The equation x-4=4(finite 7) is interpreted as a congruence: x - 4 4 7 Step 2: Solve the congruence for x. To isolate x, add 4 to both sides of the congruence: x - 4 + 4 4 + 4 7 x 8 7 Step 3: Simplify the result modulo 7. To simplify 8 7, we find the remainder when 8 is divided by 7. 8 = 1 × 7 + 1 The remainder is 1. Therefore, 8 1 7. Substituting this back into the congruence for x: x 1 7 This means x is any integer that leaves a remainder of 1 when divided by 7. For example, x could be 1, 8, 15, -6, and so on. If a single value from the set \0, 1, 2, 3, 4, 5, 6\ is expected, then x=1. The simplified form of the equation is: x 1 7