Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Advanced Algebra II: Activities and Homework » Inequalities

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Busbee's Math Materials display tagshide tags

    This collection is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy Busbee

    Click the "Busbee's Math Materials" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Inequalities

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides sample problems which develop concepts related to inequalities.

Exercise 1

4<64<6 size 12{4<6} {} (I think we can all agree on that, yes?)

  • a. Add 4 to both sides of the equation. ___________ Is it still true?
  • b. Add 44 size 12{ - 4} {} to both sides of the (original) equation. ___________ Is it still true?
  • c. Subtract 10 from both sides of the (original) equation. ___________ Is it still true?
  • d. Multiply both sides of the (original) equation by 4. ___________ Is it still true?
  • e. Divide both sides of the (original) equation by 2. ___________ Is it still true?
  • f. Multiply both sides of the (original) equation by 33 size 12{ - 3} {}. ___________ Is it still true?
  • g. Divide both sides of the (original) equation by 22 size 12{ - 2} {}. ___________ Is it still true?
  • h. In general: what operations, when performed on an inequality, reverse the inequality?

Exercise 2

2x + 3 < 7 2x + 3 < 7 size 12{2x+3<7} {}

  • a. Solve for x x.
  • b. Draw a number line below, and show where the solution set to this problem is.
  • c. Pick an xvalue x value which, according to your drawing, is inside the solution set. Plug it into the original inequality 2x+3<72x+3<7 size 12{2x+3<7} {}. Does the inequality hold true?
  • d. Pick an x-value which, according to your drawing, is outside the solution set. Plug it into the original inequality 2x+3<72x+3<7 size 12{2x+3<7} {}. Does the inequality hold true?

Exercise 3

10 x 4 10 x 4 size 12{"10" - x >= 4} {}

  • a. Solve for xx size 12{x} {}. Your first step should be adding xx size 12{x} {} to both sides, so in your final equation, xx size 12{x} {} is on the right side.
  • b. Solve for xx size 12{x} {} again from the original equation. This time, leave xx size 12{x} {} on the left side.
  • c. Did your two answers come out the same?
  • d. Draw a number line, and show where the solution set to this problem is.
  • e. Pick an xx size 12{x} {}-value which, according to your drawing, is inside the solution set. Plug it into the original inequality 10x410x4 size 12{"10" - x >= 4} {}. Does the inequality hold true?
  • f. Pick an xx size 12{x} {}-value which, according to your drawing, is outside the solution set. Plug it into the original inequality 10x410x4 size 12{"10" - x >= 4} {}. Does the inequality hold true?

Exercise 4

x = ± 4 x = ± 4 size 12{x= +- 4} {}

  • a. Rewrite this statement as two different statements, joined by “and” or “or.”
  • b. Draw a number line, and show where the solution set to this problem is.

Exercise 5

3 < x 6 3 < x 6 size 12{ - 3<x <= 6} {}

  • a. Rewrite this statement as two different statements, joined by “and” or “or.”
  • b. Draw a number line, and show where the solution set to this problem is.

Exercise 6

x > 7 x > 7 size 12{x>7} {} or x < 3 x < 3 size 12{x< - 3} {}

Draw a number line, and show where the solution set to this problem is.

Exercise 7

x > 7 x > 7 size 12{x>7} {} and x < 3 x < 3 size 12{x< - 3} {}

Draw a number line, and show where the solution set to this problem is.

Exercise 8

x < 7 x < 7 size 12{x<7} {} or x > 3 x > 3 size 12{x> - 3} {}

Draw a number line, and show where the solution set to this problem is.

Exercise 9

x > ± 4 x > ± 4 size 12{x> +- 4} {}

  • a. Rewrite this statement as two different statements, joined by “and” or “or.”
  • b. Draw a number line below, and show where the solution set to this problem is.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks