Solve the Fraction Equation: Finding X in 8/3 - 4/5x = -2/10x

To solve the equation $\frac{8}{3} - \frac{4}{5}x = -\frac{2}{10}x$, follow these steps:

• Step 1: Identify the least common denominator (LCD) of the fractions involved. The denominators are 3, 5, and 10, so the LCD is 30.
• Step 2: Multiply the entire equation by 30 to eliminate the fractions:
  $30 \times \left(\frac{8}{3} - \frac{4}{5}x\right) = 30 \times \left(-\frac{2}{10}x\right)$
• Step 3: Simplify each term:
  For $\frac{8}{3}$: $30 \times \frac{8}{3} = 10 \times 8 = 80$
  For $\frac{4}{5}x$: $30 \times \frac{4}{5}x = 6 \times 4x = 24x$
  For $-\frac{2}{10}x$: $30 \times -\frac{2}{10}x = 3 \times -2x = -6x$
• Step 4: Rewrite the equation:
  $80 - 24x = -6x$
• Step 5: Combine like terms by moving terms containing $x$ to one side:
  Subtract $-6x$ from both sides:
  $80 = 18x$
• Step 6: Solve for $x$ by dividing both sides by 18:
  $x = \frac{80}{18} = \frac{40}{9}$ after simplification.

Therefore, the solution to the problem is $x = \frac{40}{9}$.