your own words, explain why solving 4 = 2 uses the Division Property of Equality. Provide an example with your explanation. (2 points)

Answer 1

The Division Property of Equality states that when solving an equation, you can divide both sides of the equation by the same non-zero number without changing the solution. In the case of solving 4 = 2, we can use the Division Property of Equality because it allows us to manipulate the equation to find the value of the variable.

To illustrate this, let's divide both sides of the equation 4 = 2 by 2:

4/2 = 2/2,

which simplifies to:

2 = 1.

However, upon closer inspection, we realize that our initial equation 4 = 2 is false. In this case, using the Division Property of Equality led us to an incorrect solution. This illustrates the importance of verifying our solutions to make sure they are valid within the given context.

Answer 2

your own words, explain why solving 4 = 2x uses the Division Property of Equality. Provide an example with your explanation. (2 points)

Answer 3

To solve the equation 4 = 2x, the Division Property of Equality can be used. This property allows us to divide both sides of the equation by the same non-zero number to isolate the variable and find its value.

Let's solve the equation step by step:

1. Start with the equation: 4 = 2x.
2. Apply the Division Property of Equality by dividing both sides by 2: (4/2) = (2x/2).
3. Simplify both sides: 2 = x.

The simplified equation, 2 = x, tells us that the value of x is 2. By using the Division Property of Equality, we were able to isolate the variable and find its solution.

Example: Let's verify our solution by substituting x = 2 back into the original equation and see if it holds true:

4 = 2(2).

Simplifying the expression:

4 = 4.

Since the left side of the equation equals the right side, the solution x = 2 is correct. This confirms that using the Division Property of Equality led us to the correct solution.