Given the problem statement "Six less than [tex]\( 2q \)[/tex] is equal to 13 times the sum of [tex]\( q \)[/tex] and 12", we need to determine which student correctly set up the equation.
Let's break down the problem statement step-by-step.
1. Six less than [tex]\( 2q \)[/tex]:
This expression translates to [tex]\( 2q - 6 \)[/tex].
2. Is equal to:
This denotes the equality, represented by [tex]\( = \)[/tex].
3. 13 times the sum of [tex]\( q \)[/tex] and 12:
This implies [tex]\( 13 \times (q + 12) \)[/tex].
Putting it all together, the correct equation representing the problem statement is:
[tex]\[ 2q - 6 = 13(q + 12) \][/tex]
Now, let's analyze each student's equation:
- Student 1's Equation:
[tex]\[ 2(q - 6) = 13q + 12 \][/tex]
Expanding the left side:
[tex]\[ 2q - 12 = 13q + 12 \][/tex]
Clearly:
[tex]\[ 2q - 12 = 13q + 12 \][/tex]
Subtract [tex]\( 13q \)[/tex] from both sides:
[tex]\[ 2q - 13q - 12 = 12 \][/tex]
[tex]\[ -11q - 12 = 12 \][/tex]
Add 12 to both sides:
[tex]\[ -11q = 24 \][/tex]
Divide both sides by -11:
[tex]\[ q = -\frac{24}{11} \][/tex]
However this equation does not directly reflect the original problem statement correctly.
- Student 2's Equation:
[tex]\[ 2q - 6 = 13(q + 12) \][/tex]
Expanding the right side:
[tex]\[ 2q - 6 = 13q + 156 \][/tex]
This matches our original equation exactly.
Therefore, the correct statement based on the correct setup of the equation would be:
Student 2 is correct because 13 is multiplied by the quantity of [tex]\( q \)[/tex] plus 12.
We can summarize our reasoning to select the correct option:
[tex]\[ \boxed{Student \; 2 \; is \; correct\; because \; 13 \; is \; multiplied \; by \; the \; quantity \; of \; q \; plus \; 12.} \][/tex]
