Question

which expressions are equivalent to $-7z + (-2.5) + 1.5z + 3y - 3.5$?
select all that apply.
a. $-5.5z + 3y - 6$
b. $-6 + 3y + 5.5z$
c. $3y - 6 - 5.5z$
d. $3y + (-5.5z) - 2.5$
e. $-6 + 3y + (-5.5z)$

Explanation:

Step1: Combine like terms for z

We have \(-7z + 1.5z\). To combine these, we add the coefficients: \(-7 + 1.5 = -5.5\), so the z - terms combine to \(-5.5z\).

Step2: Combine the constant terms

We have \(-2.5 - 3.5\). Adding these together: \(-2.5-3.5=-6\).

Step3: Rewrite the original expression

The original expression \(-7z+(-2.5)+1.5z + 3y-3.5\) can be rewritten by combining like terms as \(3y-5.5z - 6\) (or in different orders since addition is commutative).

Now let's analyze each option:

• Option A: \(-5.5z + 3y-6\) is equivalent to our simplified expression (using commutative property of addition).
• Option B: \(-6 + 3y+5.5z\) has \(+ 5.5z\) instead of \(-5.5z\), so it is not equivalent.
• Option C: \(3y-6 - 5.5z\) is equivalent to our simplified expression (using commutative property of addition).
• Option D: \(3y+(-5.5z)-2.5\) has \(-2.5\) instead of \(-6\) (since we should have \(-2.5-3.5 = -6\)), so it is not equivalent.
• Option E: \(-6+3y+(-5.5z)\) is equivalent to our simplified expression (using commutative property of addition).

Answer:

A. \(-5.5z + 3y - 6\), C. \(3y - 6 - 5.5z\), E. \(-6 + 3y + (-5.5z)\)