1. Solve the compound inequality. Write the solution set using set-builder notation.

x + 8 < −1 or x + 3 ≥ 2

 

2. Use interval notation to express the solution set of the inequality. (If your answer is not an interval, enter the x-values(s) as a comma-separated list.)

|x + 2| ≥ 8

 

 

3.Use interval notation to express the solution set of the inequality. (If your answer is not an interval, enter the x-values(s) as a comma-separated list.)

|3x − 8| ≤ 16

 

 

 

4. Use the critical value method to solve the polynomial inequality. Use interval notation to write the solution set.

x2 + 8x > 0 

 

5.  Use the critical value method to solve the polynomial inequality. Use interval notation to write the solution set. x2 + 4x + 3 < 0

 

6.Use the critical value method to solve the rational inequality. Write the solution set in interval notation.

 

x − 4

x + 9

 > 0  7. Use the critical value method to solve the rational inequality. Write the solution set in interval notation.  

x(x − 7)

x + 2

 > 0 8. Forensic specialists can estimate the height of a deceased person from the lengths of the person's bones. These lengths are substituted into mathematical inequalities. For instance, an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur is |h − (2.47f + 54.10)| ≤ 3.72. Use this inequality to estimate the possible range of heights, rounded to the nearest 0.1 centimeter, for an adult female whose femur measures 42.25 centimeters. The height, to the nearest 0.1 cm, is from 1 cm to 2 cm.  10.  The monthly revenue R for a product is given by R = 294x − 2x2, where x is the price in dollars of each unit produced. Find the interval, in terms of x, for which the monthly revenue is greater than $0.

($0, $149]

($0, $149]

($0, $150)

[$0, $147]

($0, $147)