Final answer:
Use properties of equality, such as Commutative and Division properties, to solve equations and find the values of x. Commutative property liberates us to change the order of multiplication without affecting the product, and the Division property allows division by a non-zero number on both sides of the equation to isolate the variable, x.
Step-by-step explanation:
To solve the equations using properties of equality, one must apply certain mathematical rules that ensure the balance of the equation is maintained. Let's proceed with solving each equation step by step.
For equation (-5 × 7)25 = x(7 × 25), applying the Commutative property of multiplication, we can swap the order of multiplication without affecting the product. By simplifying both sides, we determine that x = -5.
The equation 5x = 0 can be solved using the Division property of equality. By dividing both sides by 5, we get x = 0.
In 63 = 1x, we simply identify that x = 63 by the Equivalence property.
Lastly, the equation 65 × 92 × 17 = 92 × 17 × x uses the Commutative property of multiplication to reorder the terms. Solving it, we find out that x = 65.
Throughout the solving process, eliminate terms wherever possible to simplify the algebra and check the answer to ensure it is reasonable.