Question: Solve for \( u \). \[ \frac{5}{u + 8} = 4 \] Simplify your answer as much as possible. \(…

Solve for \( u \).

\[ \frac{5}{u + 8} = 4 \]

Simplify your answer as much as possible.

\( u = \boxed{\phantom{0}} \)

Solution

To solve the equation \[ \frac{5}{u+8} = 4 \] First, multiply both sides by \(u + 8\) to get rid of the fraction: \[ 5 = 4(u + 8) \] Expand the right side: \[ 5 = 4u + 32 \] Subtract 32 from both sides to isolate the term with \(u\): \[ 5 - 32 = 4u \] \[ -27 = 4u \] Divide both sides by 4 to solve for \(u\): \[ u = \frac{-27}{4} \] So, the solution is \[ u = -\frac{27}{4} \]