Question

solve for u.
-6 = \frac{7}{u + 4}
simplify your answer as much as possible.
u = \square

Explanation:

Step1: Multiply both sides by \(u + 4\)

To eliminate the denominator, we multiply both sides of the equation \(-6=\frac{7}{u + 4}\) by \(u+4\) (assuming \(u
eq - 4\) to avoid division by zero). So we get \(-6(u + 4)=7\).

Step2: Distribute the -6

Using the distributive property \(a(b + c)=ab+ac\), where \(a=-6\), \(b = u\) and \(c = 4\), we have \(-6u-24 = 7\).

Step3: Add 24 to both sides

To isolate the term with \(u\), we add 24 to both sides of the equation. So \(-6u-24 + 24=7 + 24\), which simplifies to \(-6u=31\).

Step4: Divide by -6

To solve for \(u\), we divide both sides of the equation \(-6u = 31\) by \(-6\). So \(u=\frac{31}{-6}=-\frac{31}{6}\).

Answer:

\(u =-\frac{31}{6}\)