Question

which phrase is a description of $3k + 2$?
a 3 times the sum of $k$ and 2
b 2 more than the quotient of 3 and $k$
c 2 more than 3 more than $k$
d 2 more than 3 times $k$

Explanation:

Step1: Analyze Option A

The phrase "3 times the sum of \( k \) and 2" translates to \( 3(k + 2) \), which is not equal to \( 3k+2 \).

Step2: Analyze Option B

The phrase "2 more than the quotient of 3 and \( k \)" translates to \( \frac{3}{k}+2 \), which is not equal to \( 3k + 2 \).

Step3: Analyze Option C

The phrase "2 more than 3 more than \( k \)" translates to \( (k + 3)+2=k + 5 \), which is not equal to \( 3k+2 \).

Step4: Analyze Option D

The phrase "2 more than 3 times \( k \)" translates to \( 3k+2 \), which matches the given expression.

Answer:

D. 2 more than 3 times \( k \)