Question
Consider the sequence of steps to solve the equation: \( 3(x-4)+5 x=9 x-36 \) Given \( \Rightarrow 3(x-4)+5 x=9 x-36 \) Step \( 1 \Rightarrow 3 x-12+5 x=9 x-36 \) Step \( 2 \Rightarrow 3 x+5 x-12=9 x-36 \) Step \( 3 \Rightarrow 8 x-12=9 x-36 \) Step \( 4 \Rightarrow 8 x-8 x-12=9 x-8 x-36 \) Step \( 5 \Rightarrow 0-12=x-36 \) Step \( 6 \Rightarrow-12=x-36 \) Step \( 7 \Rightarrow-12+36=x-36+36 \) Step \( 8 \Rightarrow 24=x+0 \) Step \( 9 \Rightarrow 24=x \) Which property yields Step 6? A Additive Inverse Property B Additive Identity Property C. Addition Property of Equality
Ask by Vaughan Johnson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The property used in Step 6 is the Additive Identity Property.
Solution
The step in question transitions from:
**Step 5:** \( 0 - 12 = x - 36 \)
to
**Step 6:** \( -12 = x - 36 \)
This step simplifies \( 0 - 12 \) to \( -12 \). This simplification leverages the **Additive Identity Property**, which states that adding zero to any number leaves the number unchanged. In this case, \( 0 + (-12) = -12 \).
Therefore, the correct property used to yield Step 6 is:
**B. Additive Identity Property**
**Answer:**
**B. Additive Identity Property**
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Simplify this solution Extra Insights
To reach Step 6 from Step 5, you essentially need to isolate \( x \) on one side of the equation, which is achieved by adding \( 36 \) to both sides. This is an example of ensuring both sides of the equation remain equal while you're trying to solve for the variable. The key concept here revolves around maintaining the equality of the equation while moving terms around. In this case, the correct choice is **C. Addition Property of Equality**. This property states that if you add the same value to both sides of an equation, the equality is preserved. So, adding \( 36 \) to both sides transforms the equation accordingly, leading you to Step 6!
