Question

select the correct answer. which value of n makes this equation true? \\(\frac{3n + 3}{5} = \frac{5n - 1}{9}\\) a. \\(n = -16\\) b. \\(n = -2\\) c. \\(n = 2\\) d. \\(n = 16\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{3n + 3}{5}=\frac{5n-1}{9}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(9\times(3n + 3)=5\times(5n - 1)\).

Step2: Expand both sides

Expand the left - hand side: \(9\times3n+9\times3 = 27n+27\).
Expand the right - hand side: \(5\times5n-5\times1=25n - 5\).
So the equation becomes \(27n + 27=25n-5\).

Step3: Move the terms with n to one side and constants to the other

Subtract \(25n\) from both sides: \(27n-25n + 27=25n-25n-5\), which simplifies to \(2n+27=-5\).
Then subtract 27 from both sides: \(2n+27 - 27=-5 - 27\), so \(2n=-32\).

Step4: Solve for n

Divide both sides by 2: \(n=\frac{-32}{2}=-16\).

Answer:

A. \(n = - 16\)