Question

solve for u.
\\(\frac{6}{u - 5} = \frac{3}{2}\\)
simplify your answer as much as possible.
u = \square

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{6}{u - 5}=\frac{3}{2}\), 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 \(6\times2 = 3\times(u - 5)\).
So, \(12=3(u - 5)\).

Step2: Distribute the 3 on the right - hand side

Using the distributive property \(a(b - c)=ab - ac\), we have \(12 = 3u-15\).

Step3: Add 15 to both sides of the equation

To isolate the term with \(u\), we add 15 to both sides. \(12 + 15=3u-15 + 15\), which simplifies to \(27 = 3u\).

Step4: Divide both sides by 3

Dividing both sides of the equation \(27 = 3u\) by 3 (since to solve for \(u\), we need to get \(u\) alone, and dividing by the coefficient of \(u\) will do that), we get \(\frac{27}{3}=\frac{3u}{3}\), so \(u = 9\).

Answer:

\(u = 9\)