To solve the given equation [tex]\( 3x - 4 = -10 \)[/tex] for [tex]\( x \)[/tex], Zoe has already used the addition property of equality to isolate the variable term, resulting in [tex]\( 3x = -6 \)[/tex].
To finish solving for [tex]\( x \)[/tex], Zoe can use the following properties of equality:
1. Multiplication property of equality: This property states that if [tex]\(a = b\)[/tex], then [tex]\(a \cdot c = b \cdot c\)[/tex] for any number [tex]\(c\)[/tex]. In this context, [tex]\( 3x = -6 \)[/tex] can be solved by multiplying both sides by [tex]\(\frac{1}{3}\)[/tex], which is the same as dividing both sides by 3.
2. Division property of equality: This property states that if [tex]\(a = b\)[/tex], then [tex]\(\frac{a}{c} = \frac{b}{c}\)[/tex] for any nonzero number [tex]\(c\)[/tex]. Here, [tex]\( 3x = -6 \)[/tex] can be solved by dividing both sides by 3.
Thus, the two properties of equality that Zoe could use to finish solving for [tex]\( x \)[/tex] are:
1. Multiplication property of equality
2. Division property of equality
