The verbal sentence to represent the equation 5n/(n+3) = n-8 is: Five times a certain number divided by the sum of the number plus three is equal to the number decreased by eight.
A verbal sentence representing an equation describes an equation written in words instead of variables and numbers.
We can solve the equation as follows:
Multiplying both sides of the equation by (n+3) to clear the fraction: 5n = (n-8)(n+3)
Expanding the right-hand side using the distributive property: 5n = n^2 - 8n + 3n - 24
Combining like terms on the right-hand side: 5n = n^2 - 5n - 24
Moving all terms to one side of the equation: n^2 - 5n - 5n - 24 - 5n = 0 n^2 - 15n - 24 = 0
Factoring the quadratic equation: (n-24)(n+1) = 0
Setting each factor equal to zero and solve for n: n - 24 = 0 --> n = 24 n + 1 = 0 --> n = -1
Thus, the solutions to the equation 5n/(n+3) = n-8 are n = 24 and n = -1.