Use algebra to solve for \( x \) in the equation \( 3 x+8=9 x-7 \). If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal. \( x=\square \)

To solve the equation \( 3x + 8 = 9x - 7 \) for \( x \), follow these steps: 1. **Subtract \( 3x \) from both sides** to get all the \( x \)-terms on one side: \[ 3x + 8 - 3x = 9x - 7 - 3x \\ 8 = 6x - 7 \] 2. **Add 7 to both sides** to isolate the term with \( x \): \[ 8 + 7 = 6x - 7 + 7 \\ 15 = 6x \] 3. **Divide both sides by 6** to solve for \( x \): \[ \frac{15}{6} = x \] 4. **Simplify the fraction**: \[ x = \frac{5}{2} \] **Answer:** \[ x = \frac{5}{2} \]