Answer
x = 9
Work Step by Step
1. Given:
$\frac{5 - x}{6} + \frac{5}{6}= \frac{x}{54}$
2. Multiply by LCD (54):
54($\frac{5 - x}{6} + \frac{5}{6}) = (\frac{x}{54}$)54
3. Use distributive property to multiply:
9(5 - x) + 9(5) = x
45 - 9x + 45 = x
4. Add and subtract: -10x = -90
5. Divide: x = 9
6. Check: $\frac{5 - 9}{6} + \frac{5}{6}= \frac{9}{54}$
1/6 = 1/6, so 9 is a solution of the equation.
