Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.7, Problem 62E

To determine

**To solve: **the nonlinear inequality. Express the solution using interval notation and graph the solution set.

Expert Solution

**Given:**

The given inequality is

**Concept used:**

Guidelines for solving nonlinear inequality:

- Move all terms to one side.
- Factor the non-zero side of the inequality.
- Find the value for which each factor is zero. The number will divide the real lines into interval. List the interval determined by these numbers.
- Make a table or diagram by using test values of the signs of each factor on each interval. In the last row of the table determining the sign of the product of these factors.
- Determine the solution of the inequality from the last row of the sign table.

**Calculation:**

The given inequality can be expressed as

Firstto find the zeros of the expression in the numerator and demniminator, then

From the two zeros above, it extracts the following intervals:

Now, make a table by using test values of the signs of each factor on each interval.

+ | + | ||

+ | |||

quotient | + | + |

As it is seen that the less than or equal to 0 the interval

Hence,the solution set is

The solution set of the inequality graphed on the number line.

The graph of the non-linear inequality