Q. 24 - Precalculus Enhanced with Graphing Utilities

Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\frac{4}{y}-5=\frac{18}{2y}$

Step-by-Step Solution

Answer

The required solution is  $y=-1$. The graph of the solution is given below:

Step 1. Given information.

We have:

$\frac{4}{y}-5=\frac{18}{2y}$

Step 2. Solve the equation algebraically.

The equation is $\frac{4}{y}-5=\frac{18}{2y}$.

Simplify:

$\frac{4}{y}-5=\frac{9}{y}$

Multiply both sides by $y:$

$$\begin{gathered} \frac{4}{y}y-5y=\frac{9}{y}y \\ 4-5y=9 \end{gathered}$$

Subtract $4$ to the both sides:

$$\begin{gathered} 4-5y-4=9-4 \\ -5y=5 \end{gathered}$$

Divide both sides by $-5:$

$$\begin{gathered} \frac{-5y}{-5}=\frac{5}{-5} \\ y=-1 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $y=-1.$

Draw the graph of the equation $\frac{4}{y}-5=\frac{18}{2y}$ using the graphing utility: