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Chapter 2: Problem 124

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

Short Answer

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

Step by step solution

01

Subtract 4 from Both Sides

Subtract 4 from both sides of the equation \(x=\frac{5}{y}+4\). This gives us \(x-4=\frac{5}{y}\). This allows us to eliminate the constant from the right side of the equation.
02

Take Reciprocal of Both Sides

Take the reciprocal of both sides of the equation \(x-4=\frac{5}{y}\). The reciprocal of \(x-4\) would be \(\frac{1}{x-4}\) and the reciprocal of \(\frac{5}{y}\) would be \(\frac{y}{5}\). Therefore, we get \(\frac{1}{x-4}=\frac{y}{5}\)
03

Solve for y

To isolate y, multiply both sides of the equation by 5. Therefore, \(y= 5(\frac{1}{x-4})\) or equivalently \(y= \frac{5}{x-4}\)

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