Chapter 9.6, Problem 15CYU

To determine

To calculate: The given inequality and check solution.

Answer to Problem 15CYU

the solution is $b<0$ or $b>\frac{35}{12}$ .

Explanation of Solution

Given information: Inequality $\frac{1}{3b}+\frac{1}{4b}<\frac{1}{5}$ .

Calculation:

Inequality $\frac{1}{3b}+\frac{1}{4b}<\frac{1}{5}$ .

The excluded value for this inequality is $0$ .

Solve the related equation.

  $\frac{1}{3b}+\frac{1}{4b}=\frac{1}{5}$

The LCD for the terms is $60b$ .

Multiply both side by LCD

  $\begin{array}{l}20+15=12b\\ 12b=35\\ b=\frac{35}{12}\end{array}$

Draw vertical lines at the excluded value and at the solutions to separates the number line into intervals.

  

Now test a sample value in each interval to determine whether the values in the interval satisfy the inequality.

Test $b=-1$

  $\begin{array}{l}-\frac{1}{3}-\frac{1}{4}<\frac{1}{5}\\ -\frac{7}{12}<\frac{1}{5}\end{array}$

Test $b=1$

  $\begin{array}{l}\frac{1}{3}+\frac{1}{4}<\frac{1}{5}\\ \frac{7}{12}<\frac{1}{5}\times \end{array}$

Test $b=4$

  $\begin{array}{l}\frac{1}{12}+\frac{1}{16}<\frac{1}{5}\\ \frac{7}{48}<\frac{1}{5}\end{array}$

The statement is true for $b=-1$ and $b=4$ . Therefore, the solution is $b<0$ or $b>\frac{35}{12}$ .