INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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• ## Related Books

 1 answerLast reply by: Dr Carleen EatonSat Jan 16, 2016 10:41 PMPost by Jessie Carrillo on January 8, 2016On example 1V I also got a not true statement. But, I have a question about the step you took when subtracting 3x from both sides. Can you also add 8 to both sides in which it will create 3x >3x + 32. Afterwords, can you divided 3x in both sides in which you will have 1 > 32?

### Techniques for Multistep Inequalities

• To solve a multi-step inequality, use the same techniques that were discussed in the section on multi-step equations. For review, see the material given for that section.
• If the inequality contains grouping symbols, use the distributive property to remove these symbols and simplify the inequality.
• If the solution of an inequality leads to an inequality that is always true, the solution set of the original inequality is the set of all real numbers.
• If the solution leads to an inequality that is never true, the solution set is the empty set.

### Techniques for Multistep Inequalities

3x + 12 ≥ − 24
• 3x ≥ − 36
x ≥ − 12
5x − 20 < 115
• 5x < 135
x < 27
− 4y − 16 > 48
• − 4y > 64
y <− 16
− 2u + 14 ≤ 56
• − 2u ≤ 42
u ≥ − 21
6r − 3 > 21
• 6r > 24
r > 4
− 8p − 10 < 54
• − 8p < 64
p >− 8
− 3(c − 5) − 6 ≥ 2c + 8
• − 3c + 15 − 6 ≥ 2c + 8
• − 3c + 9 ≥ 2c + 8
• − 3c ≥ 2c − 1
• − 5c ≥ − 1
c ≥ [1/5]
− (4h + 2) − 6 < 8h + 10
• − 4h − 8 − 6 < 8h + 10
• − 4h − 14 < 8h + 10
• − 4h < 8h + 24
• − 12h < 24
h >− 2
2(3f − 5) + 4 ≥ 3(f + 4) − 10
• 6f − 10 + 4 ≥ 3f + 12 − 10
• 6f − 6 ≥ 3f + 2
• 6f ≥ 3f + 8
• 3f ≥ 8
• f[8/3]
f ≥ 3[2/3]
4(i − 4) + 1 < 6(i + 2) − 2i
• 4i − 16 + 1 < 6i + 12 − 2i
• 4i − 15 < 4i + 12
− 15 < 12
Not True
Empty Set

*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.

### Techniques for Multistep 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
• Similarity to Multistep Equations 0:16
• Negative Numbers
• Example
• Inequalities Containing Grouping Symbols 1:24
• Example
• Special Cases 2:45
• Example: All Real Numbers
• Example: Empty Set
• Example 1: Solve the Inequality 6:05
• Example 2: Solve the Inequality 7:39
• Example 3: Solve the Inequality 9:57
• Example 4: Solve the Inequality 13:56