To determine which variable expression represents the phrase "3 times the sum of twice a number and 3," let's break the phrase down step-by-step:
1. Identify the number: Let's denote the unknown number by the variable [tex]\( n \)[/tex].
2. Twice a number: Twice the number [tex]\( n \)[/tex] is written as [tex]\( 2n \)[/tex].
3. Sum of twice a number and 3: Add 3 to twice the number. This gives us [tex]\( 2n + 3 \)[/tex].
4. 3 times the sum: Finally, we need to take 3 times this sum. This is written as [tex]\( 3 \times (2n + 3) \)[/tex].
Putting it all together, the expression that represents "3 times the sum of twice a number and 3" is:
[tex]\[ 3(2n + 3) \][/tex]
Therefore, the correct variable expression from the given options is:
[tex]\[ 3(2n + 3) \][/tex]
