Alright, let's solve this problem step-by-step.
We need to determine which integer from the set [tex]\( S = \{3, 4, 5, 6\} \)[/tex] will make the equation [tex]\( 2x + 6 = 12 \)[/tex] true.
### Step-by-Step Solution:
1. Write down the equation:
[tex]\[ 2x + 6 = 12 \][/tex]
2. Solve the equation for [tex]\( x \)[/tex]:
- Subtract 6 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 2x + 6 - 6 = 12 - 6 \][/tex]
[tex]\[ 2x = 6 \][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{2x}{2} = \frac{6}{2} \][/tex]
[tex]\[ x = 3 \][/tex]
3. Verify if the solution [tex]\( x \)[/tex] is in the set [tex]\( S \)[/tex]:
The set [tex]\( S \)[/tex] is [tex]\( \{3, 4, 5, 6\} \)[/tex].
4. Check if [tex]\( x = 3 \)[/tex] is in the set [tex]\( S \)[/tex]:
Yes, [tex]\( 3 \)[/tex] is indeed a member of the set [tex]\( S \)[/tex].
### Conclusion:
The integer [tex]\( x = 3 \)[/tex] makes the equation [tex]\( 2x + 6 = 12 \)[/tex] true, and it is an element of the set [tex]\( S \)[/tex].
So, the answer is:
[tex]\[ \boxed{3} \][/tex]
