The value of x for which the expressions `11 x + 7 and 17 x - 1` become equal is ____

Options

A. `-4//3`
B. `3//4`
C. `4//3`
D. `-3//4`

Answer

To find the value of \( x \) for which the expressions \( 11x + 7 \) and \( 17x - 1 \) become equal, we can set the two expressions equal to each other and solve for \( x \).

### Step-by-Step Solution:

1. **Set the expressions equal to each other:**
\[ 11x + 7 = 17x - 1 \]

2. **Rearrange the equation to isolate \( x \):**
- First, subtract \( 11x \) from both sides:
\[ 7 = 17x - 11x - 1 \]
- This simplifies to:
\[ 7 = 6x - 1 \]

3. **Add 1 to both sides to further isolate the term with \( x \):**
\[ 7 + 1 = 6x \]
- This simplifies to:
\[ 8 = 6x \]

4. **Divide both sides by 6 to solve for \( x \):**
\[ x = \frac{8}{6} \]

5. **Simplify the fraction:**
\[ x = \frac{4}{3} \]

Thus, the value of \( x \) for which the expressions \( 11x + 7 \) and \( 17x - 1 \) become equal is \( \frac{4}{3} \).