Let's look at the steps needed to solve the equation [tex]\(3x - 4 = -10\)[/tex] and verify which properties of equality Zoe can use to finish solving for [tex]\(x\)[/tex].
Zoe has already applied the addition property of equality to isolate the term containing [tex]\(x\)[/tex]:
[tex]\[
\begin{array}{c}
3x - 4 = -10 \\
3x - 4 + 4 = -10 + 4 \\
3x = -6
\end{array}
\][/tex]
Now, Zoe has the equation [tex]\(3x = -6\)[/tex]. To solve for [tex]\(x\)[/tex], she needs to isolate [tex]\(x\)[/tex] by getting rid of the coefficient 3 in front of [tex]\(x\)[/tex].
To do that, Zoe should use the Division Property of Equality. This property allows her to divide both sides of the equation by the same non-zero number. In this case, she will divide both sides by 3:
[tex]\[
x = \frac{-6}{3}
\][/tex]
[tex]\[
x = -2
\][/tex]
Thus, the final solution for [tex]\(x\)[/tex] is [tex]\(-2\)[/tex], and the property used to finish solving for [tex]\(x\)[/tex] is the Division Property of Equality.
So, the correct answer to which properties Zoe could use to finish solving for [tex]\(x\)[/tex] is:
either the multiplication or division property of equality.
