Problem 124 - Precalculus Essentials

Question

Solve for \(y: \quad x=\frac{5}{y}+4\)

Step-by-Step Solution

Answer

The solution for \(y\) is \(y=\frac{5}{x-4}\)

Step 1: Express the equation properly

We start by subtracting 4 from both sides to isolate terms involving \(y\) on the right side of the equation. This gives us: \(x-4=\frac{5}{y}\)

Step 2: Swap sides

For easier manipulation, we switch sides so that our variable \(y\) is on the left side of the equation. This isn't necessary, but it presents the equation in the traditional format where the unknown is on the left side. Here is how the equation looks now: \(\frac{5}{y}=x-4\)

Step 3: Cross multiply

Next step is to get \(y\) out of the denominator. We multiply both sides of the equation by \(y\) to achieve this, leading to: \(5=y(x-4)\)

Step 4: Isolate \(y\)

Lastly, we solve for \(y\) by dividing both sides by \((x-4)\). This gives us the final answer: \(y=\frac{5}{x-4}\)