Algebra II Prep – Solving Compound Inequalities – Notes
Name ____________________________________________
I Can…
Date __________________
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 or b  0
2. z  3 and z  -2
3. y < –1 or y  1
4. k > 1 and k > 5
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Writing Solution Sets Examples
Write a compound inequality that describes each
graph.
5.
6.
7.
8.
Solving and Graphing Solution Sets Examples
Solve each compound inequality and then graph
the solution set.
9.
k – 3 < –7 or k + 5  8
10. 5 < 3h +2  11
11. –n < 2 or 2n – 3 > 5
12. 2c – 4 > –6 and 3c + 1 < 13
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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.
2. A number minus one is at most nine, or two
times the number is at least twenty-four.
3. 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?
4. 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
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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 or x < 3
3. g < –3 or g  4
4. –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 or x  2x – 4
8. d – 3 < 6d + 12 < 2d + 32
9. 3a + 2  5 or 7 + 3a < 2a + 6
10. n – 2 > –3 and n + 4 < 6
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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.
13. The sum of 3 times a number and 4 is between 8 and 10.
14. 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.
15. 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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