Solve the Fraction Equation: Find X in 9/11 - 8/15x = 8/22

To solve the equation $\frac{9}{11} - \frac{8}{15}x = \frac{8}{22}$, follow these steps:

• Step 1: Find the least common denominator (LCD) of 11, 15, and 22, which is 330.
• Step 2: Multiply every term in the equation by 330 to eliminate the fractions:
  $330 \times \frac{9}{11} - 330 \times \frac{8}{15}x = 330 \times \frac{8}{22}$.
• Step 3: Simplify each term:
  - For $\frac{9}{11}$: $330 \times \frac{9}{11} = 270$,
  - For $\frac{8}{15}x$: $330 \times \frac{8}{15}x = 176x$,
  - For $\frac{8}{22}$: $330 \times \frac{8}{22} = 120$.
• Step 4: Substitute back into the equation:
  $270 - 176x = 120$.
• Step 5: Isolate $x$:
  - Subtract 270 from both sides: $-176x = 120 - 270$,
  - Simplify: $-176x = -150$,
  - Divide both sides by $-176$: $x = \frac{-150}{-176} = \frac{75}{88}$.

Thus, the value of $x$ is $\frac{75}{88}$.