Question

which expressions are equivalent to $-6z + (-5.5) + 4.5z + 5y - 2.5$?
select all that apply.
a. $5y - 8 - 1.5z$
b. $-1.5z + 5y - 8$
c. $-8 + 5y + (-1.5z)$
d. $-8 + 5y + 1.5z$
e. $5y + (-1.5z) - 5.5$

Explanation:

Step1: Combine like terms for z

We have \(-6z + 4.5z\). To combine these, we subtract the coefficients: \(-6 + 4.5 = -1.5\), so \(-6z + 4.5z = -1.5z\).

Step2: Combine like terms for constants

We have \(-5.5 - 2.5\). Adding these together: \(-5.5 - 2.5 = -8\).

Step3: Rewrite the original expression

The original expression \(-6z + (-5.5) + 4.5z + 5y - 2.5\) becomes \(-1.5z + 5y - 8\) after combining like terms. Now we can rearrange the terms (using the commutative property of addition) to check each option:

• Option A: \(5y - 8 - 1.5z\) is the same as \(-1.5z + 5y - 8\) (rearranged), so it's equivalent.
• Option B: \(-1.5z + 5y - 8\) is exactly what we got, so it's equivalent.
• Option C: \(-8 + 5y + (-1.5z)\) is the same as \(-1.5z + 5y - 8\) (rearranged), so it's equivalent.
• Option D: \(-8 + 5y + 1.5z\) has \(+1.5z\) instead of \(-1.5z\), so it's not equivalent.
• Option E: \(5y + (-1.5z) - 5.5\) has \(-5.5\) instead of \(-8\) (since we combined \(-5.5 - 2.5 = -8\)), so it's not equivalent.

Answer:

A. \(5y - 8 - 1.5z\)
B. \(-1.5z + 5y - 8\)
C. \(-8 + 5y + (-1.5z)\)