Final answer:
The goal is to prove x=2 using properties of equality. Due to typos, the properties used are unclear but likely involve the Subtraction and Multiplication properties of equality. The correct form of the equation in step 2 cannot be determined without proper context or information.
Step-by-step explanation:
The objective stated in the given equation 12X = 20 - 5x is to prove that x = 2. In order to find the correct solutions and properties used, we need to follow algebraic operations that maintain the equality of both sides of the equation.
In step 1, which states "12-* = 20-5%", the property of equality applied appears to be unclear due to the typos. However, one might infer that the Subtraction property of equality is necessary to move terms with x from one side of the equation to the other, aligning the terms of x on the same side.
As for step 2, without clear information or context provided, it is impossible to determine the correct form of the equation. Options given such as "12 + 4x = 20" (option a), "12 - x = 20 - 5x" (option b), and "4x * 8" (option c) are not directly derived from the initial equation provided. Correct algebraic manipulation would result in adding 5x to both sides to gather all x terms on one side, which is not reflected in the provided options.
Regarding step 4, which states "X2", if we are to assume it means to multiply both sides of the equation by 2, then the property used here would be the Multiplication property of equality. This property ensures that when you multiply or divide both sides of an equation by the same non-zero number, the equality remains balanced.