To solve the given equation step-by-step, let's identify the proper use of the distributive property.
The equation provided is:
[tex]\[ -3(x + 2) = 21 \][/tex]
### Step-by-Step Solution:
1. Distributive Property:
The distributive property states that:
[tex]\[ a(b + c) = ab + ac \][/tex]
In our equation, we can apply the distributive property to [tex]\(-3(x + 2)\)[/tex].
Applying distributive property:
[tex]\[ -3(x + 2) = -3 \cdot x + (-3) \cdot 2 \][/tex]
[tex]\[ = -3x - 6 \][/tex]
2. This transformation gives:
[tex]\[ -3x - 6 = 21 \][/tex]
### Analysis of Options:
- Option A) [tex]\( \frac{-3(x+2)}{-3} = \frac{21}{-3} \)[/tex]
This option is indicating the step where we would divide both sides by [tex]\(-3\)[/tex], not the application of the distributive property.
- Option B) [tex]\( -3x - 6 = 21 \)[/tex]
This option correctly represents the equation after applying the distributive property, breaking down [tex]\(-3(x + 2)\)[/tex] into [tex]\(-3x - 6\)[/tex].
- Option C) [tex]\( -3x + 2 = 21 \)[/tex]
This option incorrectly applies the distributive property since the second term should be subtracted ([tex]\(-6\)[/tex]) not added [tex]\(+2\)[/tex].
- Option D) [tex]\( -3x - 6 = -63 \)[/tex]
This option is incorrect because it incorrectly transforms the equation on the right-hand side, changing 21 to -63 without any proper mathematical justification.
### Conclusion:
The step that correctly indicates the use of the distributive property when solving [tex]\(-3(x + 2) = 21\)[/tex] is:
[tex]\[ \boxed{B \, -3x - 6 = 21} \][/tex]
