Final answer:
The simplified version of the equation 2x/3 - 5x/9 - x/6 - 5x/12 = 13/2 with a common denominator of 36 results in the equation -17x = 234.
Step-by-step explanation:
The equation 2x/3 - 5x/9 - x/6 - 5x/12 = 13/2 first requires finding a common denominator to combine the terms on the left side of the equation. The common denominator for 3, 9, 6, and 12 is 36. Multiplying each term by 36/1 to eliminate the fractions gives us:
- (36/3)*2x = 24x
- (36/9)*(-5x) = -20x
- (36/6)*(-x) = -6x
- (36/12)*(-5x) = -15x
Combining these terms yields 24x - 20x - 6x - 15x, which simplifies to -17x. On the right side, multiplying 13/2 by 36 results in 234. Thus, the original equation simplifies to -17x = 234.