Algebra II Prep – Solving Compound Inequalities – Notes

Name ______Date ______

I Can… / Essential Question
Standard(s):
A-REI- Represent and solve equations and inequalities graphically
11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Key Concepts / Notes
Compound Inequality
Intersection
Union
Graphing Solution Sets Examples
Graph the solution set of each compound inequality.
  1. b > 3 orb 0
  1. z  3 and z -2
  1. y < –1 ory 1
  1. k > 1 and k > 5

Writing Solution Sets Examples
Write a compound inequality that describes each graph.

Solving and Graphing Solution Sets Examples
Solve each compound inequality and then graph the solution set.
  1. k – 3 < –7 ork + 5  8
  1. 5 < 3h +2  11
  1. –n < 2 or 2n – 3 > 5
  1. 2c – 4 > –6 and 3c + 1 < 13

Application Examples
Write and solve a compound inequality for each of the problems below and then graph the solution set.
  1. Two times a number plus one is greater than five and less than seven.
  1. A number minus one is at most nine, or two times the number is at least twenty-four.
  1. A store is offering a $30 mail-in rebate on all color printers. Lois is looking at different color printers that range in price from $175 to $260. How much can she expect to spend after the mail in rebate?
  1. About 20% of the time you sleep is spent in REM (rapid eye movement) sleep which is associated with dreaming. If an adult sleeps 7 to 9 hours, write an inequality that shows how much of the time is spent in REM sleep.

Summary, Reflection, & Analysis

Algebra II Prep – Solving Compound Inequalities – Level 1

Name ______Date ______

Directions: Graph the solution set of each compound inequality.

  1. –4 e 1 2. x > 0 orx < 3
  1. g < –3 or g  44. –3 < d and d < 2

Directions: Write a compound inequality for each graph.

5. 6.

Algebra II Prep – Solving Compound Inequalities – Level 2

Name ______Date ______

Directions: Solve each compound inequality and then graph the solution set.

7. 2x + 4  6 orx 2x – 48. d – 3 < 6d + 12 < 2d + 32

9. 3a + 2  5 or 7 + 3a < 2a + 610. n – 2 > –3 andn + 4 < 6

Algebra II Prep – Solving Compound Inequalities – Level 3

Name ______Date ______

Directions: Write a compound inequality for each problem below and then graph the solution set.

11. A number plus one is greater than negative five and less than 3.

  1. The sum of 3 times a number and 4 is between 8 and 10.
  1. A cookie contains 9 grams of fat. If you eat no less than 4 cookies, but no more than 7, write an inequality to show how many grams of fat you have consumed.
  1. The Fujita Scale (F-scale) is the official classification system for tornado damage. One factor to classify a tornado is wind speed. Use the information in the table to write an inequality for the range of wind speeds of an F3 tornado.

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