Next Generation ACCUPLACER Score Quantitative Reasoning Algebra and Statistics

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Question 1

If x ≠ 0 and x ≠ -1/4, then 2x/(4x² + x)=

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

2x/(4x² + x) simplifies to 2/(4x + 1).

To simplify the expression 2x/(4x² + x), we first factor the denominator. The denominator can be factored as x(4x + 1), allowing us to reduce the expression to 2/(4x + 1). This leads us to the correct answer: 2/(4x + 1) is equivalent to 2/4x + 1 when expressed in the form of the answer choices given.

A) 1/x + 2
This choice suggests a different form that implies a relationship between x and the terms directly, which does not align with the simplification of the original expression. The presence of 1/x does not arise from the simplification of 2x/(4x² + x), as we cannot obtain a term like this through the given algebraic manipulation.

B) 1/2x + 1
This option introduces a division by 2x, which does not correspond to the simplification of the original expression. The simplification process does not yield this form; hence, it cannot be correct.

C) 2/4x + 1
This choice correctly simplifies to the expression we derived from 2x/(4x² + x). The correct interpretation shows that we can express the final result as 1/(2x + 1/2), which confirms its validity.

D) 2/4x² + 1
This option incorrectly suggests that the entire denominator is squared, leading to a misrepresentation of the simplified expression. The original expression does not yield such a term during simplification, making this choice incorrect.

Conclusion
The expression 2x/(4x² + x) simplifies down to 2/(4x + 1) after appropriate factoring and cancellation. Choice C represents this simplification correctly, while the other choices introduce terms or configurations that do not correspond to the original expression's simplification. Understanding the simplification process is crucial for accurately identifying equivalent expressions in algebra.

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2x/(4x² + x) simplifies to 2/(4x + 1).

π/4 < x < 3π/4

y = 1/2x + 2 is the equation of the line graphed in the xy-plane.

The range of Tim's five runs is 8 seconds.

The probability that a randomly selected number from the list is less than 4 is 1/2.

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2x/(4x² + x) simplifies to 2/(4x + 1).

π/4 < x < 3π/4

y = 1/2x + 2 is the equation of the line graphed in the xy-plane.

The range of Tim's five runs is 8 seconds.

The probability that a randomly selected number from the list is less than 4 is 1/2.

Free Preview Ended

Unlock Full Access

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