If three times 1 less than a number n is the same as two times the number increased by 14, what is the value of n?

Options

A. `15`
B. `17`
C. `19`
D. `21`

Answer

To solve the equation given in the question, we will follow these steps:

1. **Translate the words into an equation**:
The phrase "three times 1 less than a number n" can be expressed as \(3(n - 1)\). The phrase "two times the number increased by 14" can be expressed as \(2n + 14\). Therefore, we can set up the equation:
\[ 3(n - 1) = 2n + 14 \]

2. **Expand the left side of the equation**:
Distributing the 3 on the left side gives us:
\[ 3n - 3 = 2n + 14 \]

3. **Rearrange the equation**:
To isolate \(n\), we will move all terms involving \(n\) to one side and constant terms to the other side. Subtract \(2n\) from both sides:
\[ 3n - 2n - 3 = 14 \]
This simplifies to:
\[ n - 3 = 14 \]

4. **Add 3 to both sides**:
To solve for \(n\), we add 3 to both sides:
\[ n = 14 + 3 \]
This simplifies to:
\[ n = 17 \]

5. **Conclusion**:
The value of \(n\) is \(17\).