9) 4 1/6 - 1 1/3x = 4x + 3 5/18

Solution:

• Convert mixed numbers to improper fractions:
  \( \frac{25}{6} - \frac{4}{3}x = 4x + \frac{59}{18} \)
• Multiply by the least common multiple of the denominators (18) to eliminate fractions:
  \( 18 \cdot \frac{25}{6} - 18 \cdot \frac{4}{3}x = 18 \cdot 4x + 18 \cdot \frac{59}{18} \)
  \( 3 \cdot 25 - 6 \cdot 4x = 72x + 59 \)
  \( 75 - 24x = 72x + 59 \)
• Isolate x terms on one side and constants on the other:
  \( 75 - 59 = 72x + 24x \)
  \( 16 = 96x \)
• Solve for x:
  \( x = \frac{16}{96} \)
  \( x = \frac{1}{6} \)

Answer: x = 1/6