Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Fundamentals of Mathematics » Solving Equations of the Form ax=b and x/a=b

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 ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • CCQ display tagshide tags

    This collection is included in aLens by: Community College of Qatar

    Comments:

    "Used as supplemental materials for developmental math courses."

    Click the "CCQ" link to see all content they endorse.

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

  • College Open Textbooks display tagshide tags

    This collection is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook Collaborative

    Comments:

    "Reviewer's Comments: 'I would recommend this text for a basic math course for students moving on to elementary algebra. The information in most chapters is useful, very clear, and easily […]"

    Click the "College Open Textbooks" link to see all content they endorse.

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

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:

    "Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and […]"

    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

  • UniqU content

    This collection is included inLens: UniqU's lens
    By: UniqU, LLC

    Click the "UniqU content" link to see all content selected in this lens.

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.
 

Solving Equations of the Form ax=b and x/a=b

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses solving equations of the form ax=bax=b size 12{"ax"=b} {} and xa=bxa=b size 12{ { {x} over {a} } =b} {}. By the end of the module students should be familiar with the multiplication/division property of equality, be able to solve equations of the form ax=bax=b size 12{ ital "ax"=b} {} and xa=bxa=b size 12{ { {x} over {a} } =b} {} and be able to use combined techniques to solve equations.

Section Overview

  • Multiplication/ Division Property of Equality
  • Combining Techniques in Equations Solving

Multiplication/ Division Property of Equality

Recall that the equal sign of an equation indicates that the number represented by the expression on the left side is the same as the number represented by the expression on the right side. From this, we can suggest the multiplication/division property of equality.

Multiplication/Division Property of Equality

Given any equation,

  1. We can obtain an equivalent equation by multiplying both sides of the equa­tion by the same nonzero number, that is, if c≠0c≠0 size 12{c <> 0} {}, then a=ba=b size 12{a=b} {} is equivalent to
     a ⋅ c = b ⋅ c a ⋅ c = b ⋅ c size 12{a cdot c=b cdot c} {}
  2. We can obtain an equivalent equation by dividing both sides of the equation by the same nonzero number, that is, if c≠0c≠0 size 12{c <> 0} {}, then a=ba=b size 12{a=b} {} is equivalent to
    a c = b c a c = b c size 12{ { {a} over {c} } = { {b} over {c} } } {}

The multiplication/division property of equality can be used to undo an association with a number that multiplies or divides the variable.

Sample Set A

Use the multiplication / division property of equality to solve each equation.

Example 1

6y=546y=54 size 12{6y="54"} {}
6 is associated with y by multiplication. Undo the association by dividing both sides by 6

6 y 6 = 54 6 6 y 6 = 54 9 6 y = 9 6 y 6 = 54 6 6 y 6 = 54 9 6 y = 9 alignl { stack { size 12{ { {6y} over {6} } = { {"54"} over {6} } } {} # size 12{ { { { {6}}y} over { { {6}}} } = { { { { {5}} { {4}}} cSup { size 8{9} } } over {6} } } {} # {} # y=9 {} } } {}

Check: When y=9y=9 size 12{y=9} {}

6 y = 54 6 y = 54 size 12{6y="54"} {}

becomes
Does 6 times 9 equal 54? Yes.,
 a true statement.

The solution to 6 y=546 y=54 size 12{6y="54"} {} is y=9y=9 size 12{y=9} {}.

Example 2

x−2=27x−2=27 size 12{ { {x} over {-2} } ="27"} {}.
-2 is associated with xx size 12{x} {} by division. Undo the association by multiplying both sides by -2.

− 2 x − 2 = − 2 27 − 2 x − 2 = − 2 27 alignl { stack { size 12{ left (-2 right ) { {x} over {-2} } = left (-2 right )"27"} {} # {} } } {}

-2 x -2 = − 2 27 -2 x -2 = − 2 27 alignl { stack { size 12{ left ( - 2 right ) { {x} over { - 2} } = left ( - 2 right )"27"} {} # {} } } {}

x = − 54 x = − 54 size 12{x= - "54"} {}

Check: When x=−54x=−54 size 12{x= - "54"} {},

x − 2 = 27 x − 2 = 27 size 12{ { {x} over { - 2} } ="27"} {}

becomes
Does negative 54 over negative 2 equal 27? Yes.
 a true statement.

The solution to x−2=27x−2=27 size 12{ { {2} over { - 2} } ="27"} {} is x=−54x=−54 size 12{x= - "54"} {}

Example 3

3a7=63a7=6 size 12{ { {3a} over {7} } =6} {}.
We will examine two methods for solving equations such as this one.

Method 1: Use of dividing out common factors.

3 a7=63 a7=6 size 12{ { {3a} over {7} } =6} {}
7 is associated with aa size 12{a} {} by division. Undo the association by multiplying both sides by 7.

7⋅ 3 a 7=7⋅67⋅ 3 a 7=7⋅6 size 12{7 cdot { {3a} over {7} } =7 cdot 6} {}
Divide out the 7’s.

7 ⋅ 3 a 7 = 42 7 ⋅ 3 a 7 = 42 size 12{ { {7}} cdot { {3a} over { { {7}}} } ="42"} {}

3 a=423 a=42 size 12{3a="42"} {}
3 is associated with aa size 12{a} {} by multiplication. Undo the association by dviding both sides by 3.

3 a 3 = 42 3 3 a 3 = 42 3 size 12{ { {3a} over {3} } = { {"42"} over {3} } } {}

3 a 3 = 14 3 a 3 = 14 size 12{ { { { {3}}a} over { { {3}}} } ="14"} {}

a = 14 a = 14 size 12{a="14"} {}

Check: When a=14a=14 size 12{a="14"} {},

3 a 7 = 6 3 a 7 = 6 size 12{ { {3a} over {7} } =6} {}

becomes
Does the quantity 3 times 14, divided by 7 equal 6? Yes.,
 a true statement.

The solution to 3 a7=63 a7=6 size 12{ { {3a} over {7} } =6} {} is a=14a=14 size 12{a="14"} {}.

Method 2: Use of reciprocals

Recall that if the product of two numbers is 1, the numbers are reciprocals. Thus 3737 size 12{ { {3} over {7} } } {} and 7373 size 12{ { {7} over {3} } } {} are reciprocals.

3 a7=63 a7=6 size 12{ { {3a} over {7} } =6} {}
Multiply both sides of the equation by 7373 size 12{ { {7} over {3} } } {}, the reciprocal of 3737 size 12{ { {3} over {7} } } {}.

7 3 ⋅ 3 a 7 = 7 3 ⋅ 6 7 3 ⋅ 3 a 7 = 7 3 ⋅ 6 size 12{ { {7} over {3} } cdot { {3a} over {7} } = { {7} over {3} } cdot 6} {}

7 1 3 1 ⋅ 3 a 1 7 1 = 7 3 1 ⋅ 6 2 1 7 1 3 1 ⋅ 3 a 1 7 1 = 7 3 1 ⋅ 6 2 1 size 12{ { { { { {7}}} cSup { size 8{1} } } over { { { {3}}} cSub { size 8{1} } } } cdot { { { { {3}}a} cSup { size 8{1} } } over { { { {7}}} cSub { size 8{1} } } } = { {7} over { { { {3}}} cSub { size 8{1} } } } cdot { { { { {6}}} cSup { size 8{2} } } over {1} } } {}

1 ⋅ a = 14 a = 14 1 ⋅ a = 14 a = 14 alignl { stack { size 12{1 cdot a="14"} {} # size 12{a="14"} {} } } {}

Notice that we get the same solution using either method.

Example 4

−8 x=24−8 x=24 size 12{-8x="24"} {}
-8 is associated with x x by multiplication. Undo the association by dividing both sides by -8.

− 8 x − 8 = 24 − 8 − 8 x − 8 = 24 − 8 alignl { stack { size 12{ { {-8x} over {-8} } = { {"24"} over {-8} } } {} # {} } } {}

− 8 x − 8 = 24 − 8 − 8 x − 8 = 24 − 8 size 12{ { {-8x} over {-8} } = { {"24"} over {-8} } } {}

x = - 3 x = - 3 size 12{x"=-"3} {}

Check: When x=−3x=−3 size 12{x= - 3} {},

− 8 x = 24 − 8 x = 24 size 12{ - 8x="24"} {}

becomes
Does negative 8 times negative 3 equal 24? Yes.,
 a true statement.

Example 5

−x=7.−x=7. size 12{-x=7 "." } {}
Since – x – x is actually −1⋅x−1⋅x size 12{-1 cdot x} {} and −1−1=1−1−1=1 size 12{ left (-1 right ) left (-1 right )=1} {}, we can isolate x x by multiplying both sides of the equation by −1−1 size 12{-1} {}.

− 1 − x = - 1 ⋅ 7 x =- 7 − 1 − x = - 1 ⋅ 7 x =- 7 alignl { stack { size 12{ left (-1 right ) left (-x right )"=-"1 cdot 7} {} # size 12{x"=-"7} {} } } {}

Check: When x=7x=7 size 12{x=7} {},

− x = 7 − x = 7 size 12{ - x=7} {}

becomes
graphics5.png

The solution to −x=7−x=7 size 12{ - x=7} {} is x=−7x=−7 size 12{x= - 7} {}.

Practice Set A

Use the multiplication/division property of equality to solve each equation. Be sure to check each solution.

Exercise 1

7x=217x=21 size 12{7x="21"} {}

Solution

x=3x=3 size 12{x=3} {}

Exercise 2

−5x=65−5x=65 size 12{-5x="65"} {}

Solution

x=-13x=-13 size 12{x"=-""13"} {}

Exercise 3

x4= -8x4= -8 size 12{ { {x} over {4} } "=-"8} {}

Solution

x=-32x=-32 size 12{x"=-""32"} {}

Exercise 4

3x8=63x8=6 size 12{ { {3x} over {8} } =6} {}

Solution

x=16x=16 size 12{x="16"} {}

Exercise 5

−y=3−y=3 size 12{-y=3} {}

Solution

y=-3y=-3 size 12{y"=-"3} {}

Exercise 6

−k=-2−k=-2 size 12{-k"=-"2} {}

Solution

k=2k=2 size 12{k=2} {}

Combining Techniques in Equation Solving

Having examined solving equations using the addition/subtraction and the multi­plication/division principles of equality, we can combine these techniques to solve more complicated equations.

When beginning to solve an equation such as 6x-4=−166x-4=−16 size 12{6 ital "x-"4= - "16"} {}, it is helpful to know which property of equality to use first, addition/subtraction or multiplication/di­vision. Recalling that in equation solving we are trying to isolate the variable (disas­sociate numbers from it), it is helpful to note the following.

To associate numbers and letters, we use the order of operations.

  1. Multiply/divide
  2. Add/subtract

To undo an association between numbers and letters, we use the order of opera­tions in reverse.

  1. Add/subtract
  2. Multiply/divide

Sample Set B

Solve each equation. (In these example problems, we will not show the checks.)

Example 6

6x−4= -166x−4= -16 size 12{6x-4"=-""16"} {}
-4 is associated with x x by subtraction. Undo the association by adding 4 to both sides.

6x − 4 + 4 = - 16 + 4 6x − 4 + 4 = - 16 + 4 size 12{6x-4+4"=-""16"+4} {}

6x= -126x= -12 size 12{6x"=-""12"} {}
6 is associated with x x by multiplication. Undo the association by dividing both sides by 6

6x 6 = − 12 6 6x 6 = − 12 6 size 12{ { {6x} over {6} } = { {-"12"} over {6} } } {}

x = - 2 x = - 2 size 12{x"=-"2} {}

Example 7

−8k+3=-45.−8k+3=-45. size 12{-8k+3"=-""45" "." } {}
3 is associated with k k by addition. Undo the association by subtracting 3 from both sides.

− 8k + 3 − 3 = -45 − 3 − 8k + 3 − 3 = -45 − 3 size 12{-8k+3-3"=-""45"-3} {}

−8k=- 48−8k=- 48 size 12{-8k"=-""48"} {}
-8 is associated with k k by multiplication. Undo the association by dividing both sides by -8.

− 8 k − 8 = − 48 − 8 − 8 k − 8 = − 48 − 8 size 12{ { {-8k} over {-8} } = { {-"48"} over {-8} } } {}

k = 6 k = 6 size 12{k=6} {}

Example 8

5m−6−4m=4m−8+3m.5m−6−4m=4m−8+3m. size 12{5m-6-4m=4m-8+3m "." } {} Begin by solving this equation by combining like terms.

m − 6 = 7 m − 8 m − 6 = 7 m − 8 size 12{m-6=7m-8} {} Choose a side on which to isolate m. Since 7 is greater than 1, we'll isolate m on the right side.
Subtract m from both sides.

− m − 6 − m = 7m − 8 − m − m − 6 − m = 7m − 8 − m size 12{-m-6-m=7m-8-m} {}

−6=6m−8−6=6m−8 size 12{-6=6m-8} {}
8 is associated with m by subtraction. Undo the association by adding 8 to both sides.

− 6 + 8 = 6m − 8 + 8 − 6 + 8 = 6m − 8 + 8 size 12{-6+8=6m-8+8} {}

2=6m2=6m size 12{2=6m} {}
6 is associated with m by multiplication. Undo the association by dividing both sides by 6.

26=6m626=6m6 size 12{ { {2} over {6} } = { {6m} over {6} } } {} Reduce.

1 3 = m 1 3 = m size 12{ { {1} over {3} } =m} {}

Notice that if we had chosen to isolate m on the left side of the equation rather than the right side, we would have proceeded as follows:

m−6=7m−8m−6=7m−8 size 12{m-6=7m-8} {}
Subtract 7m7m from both sides.

m − 6 − 7m = 7m − 8 − 7m m − 6 − 7m = 7m − 8 − 7m size 12{m-6-7m=7m-8-7m} {}

−6m−6=-8−6m−6=-8 size 12{-6m-6"=-"8} {}
Add 6 to both sides,

− 6m − 6 + 6 = -8 + 6 − 6m − 6 + 6 = -8 + 6 size 12{-6m-6+6"=-"8+6} {}

−6m=- 2−6m=- 2 size 12{-6m"=-"2} {}
Divide both sides by -6.

− 6m − 6 = − 2 − 6 − 6m − 6 = − 2 − 6 size 12{ { {-6m} over {-6} } = { {-2} over {-6} } } {}

m = 1 3 m = 1 3 size 12{m= { {1} over {3} } } {}

This is the same result as with the previous approach.

Example 9

8 x 7=-28 x 7=-2 size 12{ { {8x} over {7} } "=-"2} {}
7 is associated with x x by division. Undo the association by multiplying both sides by 7.

7 ⋅ 8x 7 = 7 − 2 7 ⋅ 8x 7 = 7 − 2 size 12{7 cdot { {8x} over {7} } =7 left (-2 right )} {}

7 ⋅ 8 x 7 = - 14 7 ⋅ 8 x 7 = - 14 size 12{ { {7}} cdot { {8x} over { { {7}}} } "=-""14"} {}

8 x=-148 x=-14 size 12{8x"=-""14"} {}
8 is associated with x x by multiplication. Undo the association by dividing both sides by 8.

8 x 8 = − 7 4 8 x 8 = − 7 4 size 12{ { { { {8}}x} over { { {8}}} } = { {-7} over {4} } } {}

x = − 7 4 x = − 7 4 size 12{x= { {-7} over {4} } } {}

Practice Set B

Solve each equation. Be sure to check each solution.

Exercise 7

5m+7=-135m+7=-13 size 12{5m+7"=-""13"} {}

Solution

m=-4m=-4 size 12{m"=-"4} {}

Exercise 8

−3a−6=9−3a−6=9 size 12{-3a-6=9} {}

Solution

a=-5a=-5 size 12{a"=-"5} {}

Exercise 9

2a+10−3a=92a+10−3a=9 size 12{2a+"10"-3a=9} {}

Solution

a=1a=1 size 12{a=1} {}

Exercise 10

11x−4−13x=4x+1411x−4−13x=4x+14 size 12{"11"x-4-"13"x=4x+"14"} {}

Solution

x=-3x=-3 size 12{x"=-"3} {}

Exercise 11

−3m+8= -5m+1−3m+8= -5m+1 size 12{-3m+8"=-"5m+1} {}

Solution

m=-72m=-72 size 12{m"=-" { {7} over {2} } } {}

Exercise 12

5y+8y−11=-115y+8y−11=-11 size 12{5y+8y-"11""=-""11"} {}

Solution

y=0y=0 size 12{y=0} {}

Exercises

Solve each equation. Be sure to check each result.

Exercise 13

7x=427x=42 size 12{7x="42"} {}

Solution

x=6x=6 size 12{x=6} {}

Exercise 14

8x=818x=81 size 12{8x="81"} {}

Exercise 15

10x=12010x=120 size 12{"10"x="120"} {}

Solution

x=12x=12 size 12{x="12"} {}

Exercise 16

11x=12111x=121 size 12{"11"x="121"} {}

Exercise 17

−6a=48−6a=48 size 12{-6a="48"} {}

Solution

a=-8a=-8 size 12{a"=-"8} {}

Exercise 18

−9y=54−9y=54 size 12{-9y="54"} {}

Exercise 19

−3y=-42−3y=-42 size 12{-3y"=-""42"} {}

Solution

y=14y=14 size 12{y="14"} {}

Exercise 20

−5a=-105−5a=-105 size 12{-5a"=-""105"} {}

Exercise 21

2m=-622m=-62 size 12{2m"=-""62"} {}

Solution

m=-31m=-31 size 12{m"=-""31"} {}

Exercise 22

3m=-543m=-54 size 12{3m"=-""54"} {}

Exercise 23

x4=7x4=7 size 12{ { {x} over {4} } =7} {}

Solution

x=28x=28 size 12{x="28"} {}

Exercise 24

y3=11y3=11 size 12{ { {y} over {3} } ="11"} {}

Exercise 25

−z6=-14−z6=-14 size 12{ { {-z} over {6} } "=-""14"} {}

Solution

z=84z=84 size 12{z="84"} {}

Exercise 26

−w5=1−w5=1 size 12{ { {-w} over {5} } =1} {}

Exercise 27

3m−1=-133m−1=-13 size 12{3m-1"=-""13"} {}

Solution

m= -4m= -4 size 12{m"=-"4} {}

Exercise 28

4x+7=-174x+7=-17 size 12{4x+7"=-""17"} {}

Exercise 29

2+9x=-72+9x=-7 size 12{2+9x"=-"7} {}

Solution

x= -1x= -1 size 12{x"=-"1} {}

Exercise 30

5−11x=275−11x=27 size 12{5-"11"x="27"} {}

Exercise 31

32=4y+632=4y+6 size 12{"32"=4y+6} {}

Solution

y=132y=132 size 12{y= { {"13"} over {2} } } {}

Exercise 32

−5+4= -8m+1−5+4= -8m+1 size 12{-5+4"=-"8m+1} {}

Exercise 33

3k+6=5k+103k+6=5k+10 size 12{3k+6=5k+"10"} {}

Solution

k=-2k=-2 size 12{k"=-"2} {}

Exercise 34

4a+16=6a+8a+64a+16=6a+8a+6 size 12{4a+"16"=6a+8a+6} {}

Exercise 35

6x+5+2x−1=9x−3x+156x+5+2x−1=9x−3x+15 size 12{6x+5+2x-1=9x-3x+"15"} {}

Solution

x=112 or 512x=112 or 512 size 12{x= { {"11"} over {2} } " or 5" { {1} over {2} } } {}

Exercise 36

−9y−8+3y+7= -7y+8y−5y+9−9y−8+3y+7= -7y+8y−5y+9 size 12{-9y-8+3y+7"=-"7y+8y-5y+9} {}

Exercise 37

−3a=a+5−3a=a+5 size 12{-3a=a+5} {}

Solution

a= -54a= -54 size 12{a"=-" { {5} over {4} } } {}

Exercise 38

5b=-2b+8b+15b=-2b+8b+1 size 12{5b"=-"2b+8b+1} {}

Exercise 39

−3m+2−8m−4= -14m+m−4−3m+2−8m−4= -14m+m−4 size 12{-3m+2-8m-4"=-""14"m+m-4} {}

Solution

m=-1m=-1 size 12{m"=-"1} {}

Exercise 40

5a+3=35a+3=3 size 12{5a+3=3} {}

Exercise 41

7x+3x=07x+3x=0 size 12{7x+3x=0} {}

Solution

x=0x=0 size 12{x=0} {}

Exercise 42

7g+4−11g=-4g+1+g7g+4−11g=-4g+1+g size 12{7g+4-"11"g"=-"4g+1+g} {}

Exercise 43

5 a7=10 5 a7=10 size 12{ { {5a} over {7} } ="10"} {}

Solution

a=14a=14 size 12{a="14"} {}

Exercise 44

2m9=42m9=4 size 12{ { {2m} over {9} } =4} {}

Exercise 45

3x4=923x4=92 size 12{ { {3x} over {4} } = { {9} over {2} } } {}

Solution

x=6x=6 size 12{x=6} {}

Exercise 46

8k3=328k3=32 size 12{ { {8k} over {3} } ="32"} {}

Exercise 47

3a8−32=03a8−32=0 size 12{ { {3a} over {8} } - { {3} over {2} } =0} {}

Solution

a=4a=4 size 12{a=4} {}

Exercise 48

5m6−253=05m6−253=0 size 12{ { {5m} over {6} } - { {"25"} over {3} } =0} {}

Exercises for Review

Exercise 49

((Reference)) Use the distributive property to compute 40⋅2840⋅28 size 12{"40" cdot "28"} {}.

Solution

4030−2=1200−80=11204030−2=1200−80=1120 size 12{"40" left ("30"-2 right )="1200"-"80"="1120"} {}

Exercise 50

((Reference)) Approximating π π by 3.14, find the approximate circumference of the circle.

A circle with radius 8cm.

Exercise 51

((Reference)) Find the area of the parallelogram.

A parallelogram with base 20cm and height 11cm.

Solution

220 sq cm

Exercise 52

((Reference)) Find the value of −34−15−2−5−34−15−2−5 size 12{ { {-3 left (4-"15" right )-2} over {-5} } } {}.

Exercise 53

((Reference)) Solve the equation x−14+8= -2.x−14+8= -2. size 12{x-"14"+8"=-"2 "." } {}

Solution

x=4x=4 size 12{x=4} {}

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