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Sagot :
Let's solve the given expression step-by-step to determine which of the given options are equivalent.
Given expression:
[tex]\[ -6n + (-12) + 4n \][/tex]
First, combine the like terms involving [tex]\( n \)[/tex]:
[tex]\[ -6n + 4n = -2n \][/tex]
Now, combine the constant term:
[tex]\[ -2n - 12 \][/tex]
So, the simplified form of the given expression is:
[tex]\[ -2n - 12 \][/tex]
Next, we need to evaluate the given options to see which are equivalent to our simplified expression.
Option A:
[tex]\[ 4(n - 3) - 6n \][/tex]
First, distribute the 4 inside the parentheses:
[tex]\[ 4n - 12 - 6n \][/tex]
Now, combine the like terms:
[tex]\[ 4n - 6n - 12 = -2n - 12 \][/tex]
This is equivalent to our simplified expression.
Option B:
[tex]\[ 2(2n - 6) \][/tex]
First, distribute the 2 inside the parentheses:
[tex]\[ 4n - 12 \][/tex]
Clearly, this is not equivalent to -2n - 12.
Since only Option A matches our simplified expression, the correct answer is:
Option A is equivalent to the given expression.
Therefore, the answer is:
[tex]\[ \boxed{A} \][/tex]
Given expression:
[tex]\[ -6n + (-12) + 4n \][/tex]
First, combine the like terms involving [tex]\( n \)[/tex]:
[tex]\[ -6n + 4n = -2n \][/tex]
Now, combine the constant term:
[tex]\[ -2n - 12 \][/tex]
So, the simplified form of the given expression is:
[tex]\[ -2n - 12 \][/tex]
Next, we need to evaluate the given options to see which are equivalent to our simplified expression.
Option A:
[tex]\[ 4(n - 3) - 6n \][/tex]
First, distribute the 4 inside the parentheses:
[tex]\[ 4n - 12 - 6n \][/tex]
Now, combine the like terms:
[tex]\[ 4n - 6n - 12 = -2n - 12 \][/tex]
This is equivalent to our simplified expression.
Option B:
[tex]\[ 2(2n - 6) \][/tex]
First, distribute the 2 inside the parentheses:
[tex]\[ 4n - 12 \][/tex]
Clearly, this is not equivalent to -2n - 12.
Since only Option A matches our simplified expression, the correct answer is:
Option A is equivalent to the given expression.
Therefore, the answer is:
[tex]\[ \boxed{A} \][/tex]
Answer: A. 4 (n-3) -6n
Step-by-step explanation:
Solve this equation by simplifying your answer choices:
A. Distribute 4 into the equation within the parenthesis. You are left with
4n -12 -6n, which is the same as -6n + (-12) +4n. A is a viable answer
B. Distribute 2 into the equation within the parenthesis. You are left with 4n-12, however this is not the same as -6n + (-12) +4n. B is not an answer
C. C is not answer answer because A qualifies as an answer.
The answer is A
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