To solve the problem, let's follow these steps:
1. Understand the problem statement:
- We have a number [tex]\( n \)[/tex].
- We are adding this number [tex]\( n \)[/tex] to 15 less than 3 times itself.
- The result of this addition is 101.
2. Translate the problem into a mathematical expression:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- Adding the number [tex]\( n \)[/tex] to this, we get: [tex]\( n + (3n - 15) \)[/tex].
- The result of this expression is 101.
3. Formulate the equation:
- The mathematical expression we created needs to equal 101.
- Therefore, we can write the equation as:
[tex]\[
n + (3n - 15) = 101
\][/tex]
4. Simplify the equation:
- Combine like terms on the left side: [tex]\( n + 3n - 15 \)[/tex].
- This simplifies to [tex]\( 4n - 15 \)[/tex].
5. Equation in standard form:
- The simplified equation is:
[tex]\[
4n - 15 = 101
\][/tex]
6. Rearrange the standard form equation to match the options:
- Combining like terms before equating gives:
[tex]\[
3n - 15 + n = 101
\][/tex]
- This is a match for one of the provided options.
Therefore, the correct equation to solve for [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This corresponds to the first option:
[tex]\[ 3n - 15 + n = 101 \][/tex]
