Final answer:
To solve the equation 3/4p = 4/5p + 1/2, find a common denominator, combine like terms, and isolate the variable p to one side of the equation. The solution is p = -10.
Step-by-step explanation:
To solve the equation 3/4p = 4/5p + 1/2, we want to isolate the variable p on one side. First, we can simplify the equation by finding a common denominator for the fractions. The least common denominator is 20, so we can rewrite the equation as (15p)/20 = (16p + 10)/20. Now, we can combine the fractions on the right side of the equation by adding their numerators: (15p) = (16p + 10). Next, we can move the variable terms to one side and the constant terms to the other side of the equation: 15p - 16p = 10. Simplifying, we get -p = 10. Finally, we divide both sides of the equation by -1 to solve for p: p = -10.