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

## Discussion

## Study Guides

## Practice Questions

## Download Lecture Slides

## Table of Contents

## Related Books

### Solving Inequalities by Multiplying

- Solving one-step and two-step inequalities is similar to solving one-step and two-step equations.
- Use the Multiplication Property of Inequality to inverse division in order to isolate the variable and solve the inequality.
- When multiplying or dividing each side of the inequality by a negative number you must reverse the inequality sign to keep the inequality true.

### Solving Inequalities by Multiplying

[x/0.2] ≥ 8. Solve for x.

- x ≥ 8 ×0.2

x ≥ 1.6

[x/5] ≤ 3. Solve for x.

- x ≤ 3 ×5

x ≤ 15

4.5 < [x/2]. Solve for x.

- 4.5 ×2 < x

x > 9

0.25 > [x/8]. Solve for x.

- 0.25 ×8 > x

x < 2

[x/( − 3)]7. Solve for x.

- x ≤ 7 ×( − 3)

x ≤ − 21

[x/( − 9)]0.3. Solve for x.

- x ≤ 0.3 ×( − 9)

x ≤ − 2.7

4.5 < [x/( − 2)]. Solve for x.

- 4.5 ×( − 2) > x

x <− 9

5 > [x/( − 0.05)]. Solve for x.

- 5 ×( − 0.05) < x

x >− 0.25

A sports district league has 5 teams in the district. Each team must have at least 10 players. Write and solve an inequality to find the number of players that need to sign up for the league.

- Let p = number of players that need to sign up for the league.
- [p/5] ≤ 10
- p ≤ 10 ×5

p ≤ 50 players

Write an inequality to represent the word phrase; then, solve the inequality and graph it. The quotient of a number x and - 12 is greater than - 2.

- [x/( − 12)] >− 2
- x <− 2 ×( − 12)

x < 24

*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 Multiplying

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
- What You'll Learn and Why
- Vocabulary
- Multiplying by a Positive Number
- Multiplying by a Positive Number
- Multiplying by a Negative Number
- Extra Example 1: Bowling League
- Extra Example 2: Street Performers
- Extra Example 3: Write and Solve the Inequality
- Extra Example 4: Solve and Graph the System of Inequalities

- Intro 0:00
- What You'll Learn and Why 0:07
- Topics Overview
- Vocabulary 0:17
- Multiplication Property of Inequality
- Multiplying by a Positive Number 1:25
- Example: Write and Solve an Inequality
- Multiplying by a Positive Number 3:38
- Example: Write and Solve an Inequality
- Multiplying by a Negative Number 5:42
- Example: Solve x/-4 > 28
- Example: Solve (-1/2)y < -8
- Example: t/-7 < 5
- Extra Example 1: Bowling League 7:12
- Extra Example 2: Street Performers 8:27
- Extra Example 3: Write and Solve the Inequality 9:52
- Extra Example 4: Solve and Graph the System of Inequalities 11:26

2 answers

Last reply by: Cory Kolesnikowicz

Mon Jun 9, 2014 9:39 PM

Post by Tami Cummins on June 30, 2013

Your inequality sign is backward. It says the teams must have at least 15 bowlers. Each team could have more.

1 answer

Last reply by: Cory Kolesnikowicz

Mon Jun 9, 2014 9:25 PM

Post by Tom Byrd on October 6, 2011

I would have written this as " P is greater than or equal to 2.6 times 8" since each piece is "at least 2.6 feet long". My answer is "P is greater than or equal to 20.8". Can you tell me where I am going wrong?