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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Lecture Comments (2)

1 answer

Last reply by: Taylor Wright
Wed Jun 19, 2013 11:52 PM

Post by Taylor Wright on June 19, 2013

I'm confused, why did you put 3x-2 is less than or = 2 ?

Shouldn't it be 7?

Compound Inequalities

  • A compound inequality combines two inequalities using either “and” or “or”. First solve each inequality separately. If “and” was used, the solution set is the set of all numbers in both solution sets of the two inequalities. If “or” was used, the solution is all numbers in either or both of the solution sets of the two inequalities.
  • The solution of a compound inequality can be found by simplifying each inequality algebraically and then graphing the simplified inequalities.
  • Describe the solution set of a compound inequality using either a number line or set builder notation.

Compound Inequalities

Solve the compound inequality:
3x − 2 < 74x + 6 > 10
  • 3x − 2 < 7
  • 3x < 9
  • x < 3
  • 4x + 6 > 10
  • 4x > 4
  • x > 1
1 < x < 3
7s − 5 ≤ 16 3x + 10 ≥ 22
  • 7s − 5 ≤ 16
  • 7s ≤ 21
  • s ≤ 3
  • 3s + 10 ≥ 22
  • 3s ≥ 12
  • s ≥ 4
3 ≥ s ≥ 4
6d + 2 > 87d − 5 < 9
  • 6d + 2 > 8
  • 6d > 6
  • d > 1
  • 7d − 5 < 9
  • 7d < 14
  • d < 2
1 < d < 2
3k − 4 ≤ 8
7k − 7 > 35
  • 3k − 4 ≤ 8
  • 3k ≤ 12
  • k ≤ 4
  • 7k − 7 > 14
  • 7k > 21
  • k > 3
3 < k ≤ 4
2n − 3 < 5
4n − 1 ≥ 19
  • 2n − 3 < 5
  • 2n < 8
  • n < 4
  • 4n − 1 ≥ 19
  • 4n ≥ 20
  • n ≥ 5
n < 4 and n ≥ 5
4 < n ≥ 5
8m − 2 ≤ 22
5m − 4 ≥ 51
  • 8m − 2 ≤ 22
  • 8m ≤ 24
  • m ≤ 3
  • 5m − 4 ≥ 51
  • 5m ≥ 55
  • m ≥ 11
m ≤ 3 and m ≥ 11
3 ≥ m ≥ 11
− 9 < 6x − 7 < 11
  • − 9 < 6x − 7 and 6x − 7 < 11
  • − 9 < 6x − 7
  • − 2 < 6x
  • − [2/6] < x
  • − [1/3] < x
  • 6x − 7 < 11
  • 6x < 18
  • x < 3
− [1/3] < x < 3
− 34 ≥ 6x + 2 > 26
  • − 34 ≥ 6x + 26x + 2 > 26
  • − 34 ≥ 6x + 2
  • − 36 ≥ 6x
  • − 6 ≥ x
  • 6x + 2 > 26
  • 6x > 24
  • x > 4
− 6 ≥ x > 4
Solve the compound inequality:
− 2h − 11 > 9 or − 5h + 7 ≤ − 13
  • − 2h − 11 > 9
  • − 2h > 20
  • h < − 10
  • − 5h + 7 ≤ − 13
  • − 5h ≤ − 20
  • h ≥ 4
h < − 10 or h ≥ 4
− 5x − 4 ≥ 11 or − 3x + 12 < 36
  • − 5x − 4 ≥ 11
  • − 5x ≥ 15
  • x ≤ − 3
  • − 3x + 12 < 36
  • − 3x < 24
  • x > − 8
x > − 8 or x ≤ − 3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Compound Inequalities

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • What is a Compound Inequality 0:07
    • Joined by 'And' or 'Or'
  • Inequalities Combined by 'And' 0:36
    • Intersection/Overlap
    • Example
  • Inequalities Combined by 'Or' 4:23
    • Union
    • Example
  • Example 1: Solve the Inequality 6:39
  • Example 2: Solve the Inequality 11:30
  • Example 3: Solve the Inequality 13:43
  • Example 4: Solve the Inequality 18:19