Compound Inequalities Bonus Worksheet
ALGEBRA 1 • UNIT 1 EXTENSION QUIZ BONUS CHALLENGE PAGE 1 OF 1
Compound Inequalities
Advanced Modeling • Bonus Problems
Name:
Date:
Period:
Bonus Instructions: Define variables, set up algebraic compound inequalities, and show every inverse operation.
Earn up to +10 Points
1
Find three consecutive odd integers such that five less than twice their sum is strictly between 61 and 85.
+4 PTS
1. Define Variables
Let 1st odd int =
Let 2nd odd int =
Let 3rd odd int =
Sum in terms of n: _______
2. Write & Solve Inequality
Range for n: ____________
3. The Three Integers
{ , , }
Check: 2(Sum) − 5 =
2
Five more than twice a number is either at most −3 or at least 11.
Write a compound inequality, solve for all possible values of the number, and graph the solution set.
+3 PTS
Variable:
Compound Inequality:
Solve "At Most −3" ≤
Branch 1: _________________________
Solve "At Least 11" ≥
Branch 2: _________________________
Final Solution: Solution:
-8 -6 -4 -2 0 2 4 6 8
3
Fourteen less than a number is between −6 and 11.
Find the range of numbers that make this statement true.
+3 PTS
Variable:
Inequality:
Answer:
Algebra 1 • Lesson 1-6 Extension Show all inverse operations clearly for full credit Page 1 of 1
Compound Inequalities Answer Key
ALGEBRA 1 • UNIT 1 EXTENSION TEACHER ANSWER KEY PAGE 1 OF 1
Compound Inequalities
Full Worked Solutions • Scoring Rubric
Total Points 10 Pts Bonus
+10 Max
Grading Note: Award partial credit for correct algebraic setups even if minor arithmetic errors occur.
P1: 4 pts • P2: 3 pts • P3: 3 pts
1
Find three consecutive odd integers such that five less than twice their sum is strictly between 61 and 85.
+4 PTS
1. Variable Setup (1 pt)
1st int: n
2nd int: n + 2
3rd int: n + 4
Sum = 3n + 6
2. Algebraic Steps (2 pts)
\(61 < 2(3n + 6) - 5 < 85\) (1 pt)
\(61 < 6n + 7 < 85\)
\(54 < 6n < 78\)
\(9 < n < 13\) (1 pt)
n must be an odd integer
3. Final Solution (1 pt)
Since \(n \in (9, 13)\) is odd:
{ 11, 13, 15 }
✓ Check: 2(39) − 5 = 73 ∈ (61, 85)
2
Five more than twice a number is either at most −3 or at least 11.
Write a compound inequality, solve for all possible values of the number, and graph the solution set.
+3 PTS
Variable (0.5 pt): Let x = the number
Inequality (0.5 pt): 2x + 5 ≤ −3 or 2x + 5 ≥ 11
Left Branch (≤ −3) • 0.5 pt ≤
\(2x + 5 \le -3\)
\(2x \le -8\)
\(x \le -4\)
Right Branch (≥ 11) • 0.5 pt ≥
\(2x + 5 \ge 11\)
\(2x \ge 6\)
\(x \ge 3\)
Solution (0.5 pt) & Graph (0.5 pt): x ≤ −4 or x ≥ 3 (−∞, −4] ∪ [3, ∞)
-8 -6 -4 -2 0 2 3 4 6 8
3
Fourteen less than a number is between −6 and 11.
Find the range of numbers that make this statement true.
+3 PTS
Variable (0.5 pt): Let n = the number
Inequality (1 pt): −6 < n − 14 < 11
Solve (0.5 pt):−6 < n − 14 < 11
Add 14:−6 + 14 < n − 14 + 14 < 11 + 14
Result:8 < n < 25
Key Misconception:
Watch for students writing \(14 - n\) instead of \(n - 14\) for "fourteen less than a number".
Answer (1 pt): 8 < n < 25 or (8, 25)
Algebra 1 • Lesson 1-6 Extension Answer Key • For Teacher Facilitation and Grading Page 1 of 1
