Let's look at how the given equation is solved step-by-step to complete the statements correctly.
1. The initial equation provided is [tex]\(3x - 10 = -16\)[/tex].
2. In step 2, the equation is [tex]\(3x - 10 + 10 = -16 + 10\)[/tex]. To simplify the equation, we added 10 to both sides. This preserves equality because whatever you do to one side of the equation, you must do to the other side. This application is known as the Addition Property of Equality.
3. Simplifying step 2, we get [tex]\(3x = -6\)[/tex].
4. In step 4, [tex]\(\frac{3x}{3} = \frac{-6}{3}\)[/tex]. To isolate [tex]\(x\)[/tex], we divided both sides by 3. This application is known as the Division Property of Equality.
5. Simplifying step 4, we get [tex]\(x = -2\)[/tex].
Using this detailed walkthrough, we can determine the correct properties of equality applied in each step.
So,
1. In step 2, the Addition property of equality was applied.
2. In step 4, the Division property of equality was applied.
