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Q. 24

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Found in: Page 29

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.$\frac{4}{y}-5=\frac{18}{2y}$

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

See the step by step solution

## 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 $y:$

$\frac{4}{y}y-5y=\frac{9}{y}y\phantom{\rule{0ex}{0ex}}4-5y=9$

Subtract $4$ to the both sides:

$4-5y-4=9-4\phantom{\rule{0ex}{0ex}}-5y=5$

Divide both sides by $-5:$

$\frac{-5y}{-5}=\frac{5}{-5}\phantom{\rule{0ex}{0ex}}y=-1$

## 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: