2. Read the phrase below. the quotient of three less than a number and six more than four × a number Which expression is equivalent to this phrase?
Answer: C
The expression equivalent to the phrase is (x-3)/(4x + 6).
The phrase describes the quotient of "three less than a number" (x - 3) and "six more than four times a number" (4x + 6). Therefore, the correct expression is (x - 3)/(4x + 6).
A) (3-x)/(4x + 6)
This option incorrectly represents "three less than a number" as (3 - x) instead of (x - 3). The numerator needs to reflect a reduction from the variable x, making this option incorrect.
B) (x - 3)(4x + 6)
This option suggests multiplication instead of a quotient, which does not align with the phrase's description. The phrase specifically calls for a division between the two expressions, making this option incorrect.
C) (x-3)/(4x + 6)
This option accurately represents the phrase by placing "three less than a number" in the numerator as (x - 3) and "six more than four times a number" in the denominator as (4x + 6). This is the correct expression.
D) 4x - 3 + 6
This option does not provide a quotient but rather presents a simplified expression that does not correspond to the original phrase. It fails to capture the division aspect required by the phrase, making it incorrect.
Conclusion
The correct option, (x-3)/(4x + 6), directly reflects the mathematical meaning of the phrase by maintaining the required structure of a quotient. All other options fail to accurately represent the phrase either through incorrect operations or misinterpretation of the components involved.