Are the following expressions equivalent? Prove your answer.

8(2z-3) and 16z - 3

8(2z-3) = 16z - 24

The answer is no? Not equivalent

You're right. They are not equivalent.

Thank u Ms. Sue

You're welcome, Amy.

To determine if the expressions 8(2z-3) and 16z-3 are equivalent, we can simplify both expressions and check if they yield the same result.

Let's start with the expression 8(2z-3):

Step 1: Apply the distributive property, which states that a(b+c) = ab + ac.
So, we have: 8 * 2z + 8 * (-3).
Simplifying further: 16z - 24.

Next, let's simplify the expression 16z - 3:

There's nothing much we can do with this expression as it is already simplified.

If we compare the two expressions:

8(2z-3) = 16z - 24
16z - 3

We can see that 8(2z-3) simplifies to 16z - 24. So, the expressions 8(2z-3) and 16z-3 are not equivalent.

To prove this, you can choose a value for z, substitute it into both expressions, and compare the results. For example, let's say z = 5:

8(2 * 5 - 3) = 16 * 5 - 24
8(10 - 3) = 16 * 5 - 24
8 * 7 = 80 - 24
56 = 56

Now, let's compare it to the other expression:

16 * 5 - 3 = 80 - 3
80 - 3 = 77

Since 56 is not equal to 77, this tells us that the two expressions are not equivalent.