Certainly! Let's analyze the steps provided in the table and identify which property of equality was applied in each relevant step.
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Step 1: [tex]\(3x - 10 = -16\)[/tex]
This is the original equation.
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Step 2: [tex]\(3x - 10 + 10 = -16 + 10\)[/tex]
In this step, 10 is added to both sides of the equation. This is done to isolate the term containing [tex]\(x\)[/tex] on one side of the equation. The property of equality applied here is called the Addition Property of Equality. By adding the same number to both sides of the equation, the equality is preserved.
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Step 3: [tex]\(3x = -6\)[/tex]
In this step, the equation simplifies as the [tex]\(-10\)[/tex] and [tex]\(+10\)[/tex] on the left side cancel each other out.
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Step 4: [tex]\(\frac{3x}{3} = \frac{-6}{3}\)[/tex]
In this step, both sides of the equation are divided by 3 to solve for [tex]\(x\)[/tex]. The property of equality applied here is the Division Property of Equality. By dividing both sides of an equation by the same nonzero number, the equality is preserved.
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Step 5: [tex]\(x = -2\)[/tex]
In this step, the result of the division is shown, and the value of [tex]\(x\)[/tex] is found to be [tex]\(-2\)[/tex].
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As a result, the correct answers for each statement are:
1. In step 2, the Addition property of equality was applied.
2. In step 4, the Division property of equality was applied.
