Final answer:
The correct algebraic equation is '5(x - 20) = 0.5(4 + 4x)' which, when solved, gives x = 34. Incorrect application of algebraic rules would result in the wrong solution.
Step-by-step explanation:
The given problem requires translating a word problem into an algebraic equation and solving it. The correct equation to represent the relationship described in the question is 5 times the difference of a number (x) and 20 is the same as half the sum of 4 more than 4 times that number.
This translates to the algebraic equation: 5(x - 20) = 0.5(4 + 4x). Solving for x involves expanding both sides, combining like terms, and isolating the variable x.
Now, we will solve for x step by step:
- Distribute 5 on the left side: 5x - 100 = 0.5(4 + 4x).
- Distribute 0.5 on the right side: 5x - 100 = 2 + 2x.
- Subtract 2x from both sides: 3x - 100 = 2.
- Add 100 to both sides: 3x = 102.
- Divide both sides by 3: x = 34.
Therefore, x = 34 is the solution to the correct equation.
As per the rules of mathematics, incorrect application of these steps would lead to an incorrect solution. Any deviation from the proper algebraic translation or arithmetic procedure would be an error in the calculation akin to a basic arithmetic mistake.