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.