For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Solving Inequalities by Dividing

- The steps for solving one-step and two-step equations are similar to those for solving inequalities.
- Use the Division Property of Inequality to cancel out multiplication, to isolate the variable, and to solve the inequality.
- A negative number is the opposite of a positive number so when you divide each side of an inequality by a negative number, in order for the inequality to stay true, you must reverse the direction of the inequality sign.

### Solving Inequalities by Dividing

5x ≥ 25. Solve for x.

- x ≥ 25 ÷5

x ≥ 5

9x ≤ 18. Solve for x.

- x ≤ 18 ÷9

x ≤ 2

10x < 0.4. Solve for x.

- x < 0.4 ÷10

x < 0.04

9.5 > 5x. Solve for x.

- 9.5 ÷5 > x

x < 1.9

−5x ≥ 725. Solve for x.

- x ≤ 725 ÷( − 5)

x ≤ − 145

− 2x < [2/5]. Solve for x.

- x > [2/5] ÷( − 2)
- x > [2/5] ×( − [1/2])

x > − [1/5]

[5/7] < − 4x. Solve for x.

- [5/7] ÷( − 4) > x
- [5/7] ×( − [1/4]) > x

− [7/28] > x

0.4 ≤ − 0.1x. Solve for x.

- 0.4 ÷( − 0.1)x

− 4x

A classroom can hold as many as 35 students. A city has 1612 students. How many classrooms does the city need?

- Let c = number of classrooms needed for the city.
- 35c ≥ 1612
- c ≥ 1612 ÷35
- c ≥ 46.06

At least 47 classrooms

An elevator can safely carry as much as 2800 lb. The makers of the elevator assumed 350 lb to be the maximum weight of one person. How many people can this elevator safely carry?

- 350p ≤ 2800
- p ≤ 2800 ÷350
- p ≤ 8

At most 8 people

*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

### Solving Inequalities by Dividing

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 You'll Learn and Why 0:06
- Topics Overview
- Vocabulary 0:22
- Division Property of Inequality
- Example: 3x > 6
- Dividing by a Positive Number 1:08
- Example: Hotel Elevator
- Dividing by a Negative Number 2:29
- Example: Solve -6x ≥ -18
- Example: Suppose x = 2
- Dividing by a Negative Number 4:58
- Example: Solve -3t ≥ 51
- Example: Solve -8m < -56
- Extra Example 1: Photo Album 5:49
- Extra Example 2: Banquet 8:05
- Extra Example 3: Solve -0.5x > 18 9:24
- Extra Example 4: How Many Crates can the Crane Lift? 10:30

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