QQuestionMathematics
QuestionMathematics
"Which algebraic expression is equivalent to the expression below?
9(4x + 8) – 4
A. 36x + 36
B. 36x + 4
C. 36x + 68
D. 36x + 72"
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Answer
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Step 1:: Distribute the 9 in the given expression, 9(4x + 8).
This will result in: 9(4x) + 9(8) = 36x + 72
Step 2:: Subtract 72 from both sides of the equation to isolate the term with x:
36x + 72 - 72 = 9x
Step 3:: The expression 9x does not match any of the answer choices, so we need to factor out 36 from this term:
36x = 36 * (x)
Step 4:: Now, the expression is in the form of answer choice A, 36x + 36.
However, we need to verify if this is indeed the correct answer by checking if it is equivalent to the original expression.
Step 5:: Expand 36(x + 1):
36(x) + 36(1) = 36x + 36
Step 6:: Comparing this expression with the original expression, we find that they are not equivalent.
Thus, answer choice A is incorrect.
Step 7:: We need to repeat the process of factoring for the other answer choices.
For answer choice B, 36x + 4, we can't factor out 4 from the first term, so we can eliminate this choice.
Step 8:: For answer choice C, 36x + 68, we can't factor out 68 from the first term, so we can eliminate this choice as well.
Step 9:: For answer choice D, 36x + 72, we can't factor out 72 from the first term, so we can eliminate this choice as well.
Step 10:: None of the answer choices are equivalent to the original expression.
However, upon further inspection, we can see that the original expression, 9(4x + 8) - 4, can be simplified to 36(x + 2) - 4. This expression is not listed among the answer choices, but it is equivalent to the original expression.
Final Answer
The expression equivalent to the given expression is 36(x + 2) - 4, which is not listed among the answer choices.
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