12) 7/12x + 4/9 = 1/4x - 5/6

Solution:

• Multiply by the least common multiple of the denominators (36) to eliminate fractions:
  \( 36 \cdot \frac{7}{12}x + 36 \cdot \frac{4}{9} = 36 \cdot \frac{1}{4}x - 36 \cdot \frac{5}{6} \)
  \( 3 \cdot 7x + 4 \cdot 4 = 9 \cdot x - 6 \cdot 5 \)
  \( 21x + 16 = 9x - 30 \)
• Isolate x terms on one side and constants on the other:
  \( 21x - 9x = -30 - 16 \)
  \( 12x = -46 \)
• Solve for x:
  \( x = \frac{-46}{12} \)
  \( x = -\frac{23}{6} \)

Answer: x = -23/6