# Connexions

You are here: Home » Content » Maths Grade 10 Rought draft » Solving linear equations

### 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?

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

#### 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.
• FETMaths

This module is included inLens: Siyavula: Mathematics (Gr. 10-12)
By: Siyavula

Review Status: In Review

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

Click the 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.

Inside Collection (Textbook):

Textbook by: Nerk van Rossum. E-mail the author

# Solving linear equations

## Equations and inequalities: Solving linear equations

The simplest equation to solve is a linear equation. A linear equation is an equation where the power of the variable(letter, e.g. xx) is 1(one). The following are examples of linear equations.

2 x + 2 = 1 2 - x 3 x + 1 = 2 4 3 x - 6 = 7 x + 2 2 x + 2 = 1 2 - x 3 x + 1 = 2 4 3 x - 6 = 7 x + 2
(1)

In this section, we will learn how to find the value of the variable that makes both sides of the linear equation true. For example, what value of xx makes both sides of the very simple equation, x+1=1x+1=1 true.

Since the definition of a linear equation is that if the variable has a highest power of one (1), there is at most one solution or root for the equation.

This section relies on all the methods we have already discussed: multiplying out expressions, grouping terms and factorisation. Make sure that you are comfortable with these methods, before trying out the work in the rest of this chapter.

2 x + 2 = 1 2 x = 1 - 2 ( like terms together ) 2 x = - 1 ( simplified as much as possible ) 2 x + 2 = 1 2 x = 1 - 2 ( like terms together ) 2 x = - 1 ( simplified as much as possible )
(2)

Now we see that 2x=-12x=-1. This means if we divide both sides by 2, we will get:

x = - 1 2 x = - 1 2
(3)

If we substitute x=-12x=-12, back into the original equation, we get:

LHS = 2 x + 2 = 2 ( - 1 2 ) + 2 = - 1 + 2 = 1 and RHS = 1 LHS = 2 x + 2 = 2 ( - 1 2 ) + 2 = - 1 + 2 = 1 and RHS = 1
(4)

That is all that there is to solving linear equations.

### Tip: Solving Equations:

When you have found the solution to an equation, substitute the solution into the original equation, to check your answer.

### Method: Solving Linear Equations

The general steps to solve linear equations are:

1. Expand brackets: Expand (Remove) all brackets that are in the equation.
2. Rearrange: "Move" all terms with the variable to the left hand side of the equation, and all constant terms (the numbers) to the right hand side of the equals sign. Bearing in mind that the sign of the terms will change from (++) to (--) or vice versa, as they "cross over" the equals sign.
3. Group like terms: Group all like terms together and simplify as much as possible.
4. Factorise: If necessary factorise.
5. Write solution: Find the solution and write down the answer(s).
6. Check: Substitute solution into original equation to check answer.

Figure 1
Khan academy video on equations - 1

#### Exercise 1: Solving Linear Equations

Solve for xx: 4-x=44-x=4

#### Exercise 2: Solving Linear Equations

Solve for xx: 4(2x-9)-4x=4-6x4(2x-9)-4x=4-6x

#### Exercise 3: Solving Linear Equations

Solve for xx: 2-x3x+1=22-x3x+1=2

#### Exercise 4: Solving Linear Equations

Solve for xx: 43x-6=7x+243x-6=7x+2

#### Solving Linear Equations

1. Solve for yy: 2y-3=72y-3=7

2. Solve for yy: -3y=0-3y=0

3. Solve for yy: 4y=164y=16

4. Solve for yy: 12y+0=14412y+0=144

5. Solve for yy: 7+5y=627+5y=62

6. Solve for xx: 55=5x+3455=5x+34

7. Solve for xx: 5x=3x+455x=3x+45

8. Solve for xx: 23x-12=6+2x23x-12=6+2x

9. Solve for xx: 12-6x+34x=2x-24-6412-6x+34x=2x-24-64

10. Solve for xx: 6x+3x=4-5(2x-3)6x+3x=4-5(2x-3)

11. Solve for pp: 18-2p=p+918-2p=p+9

12. Solve for pp: 4p=16244p=1624

13. Solve for pp: 41=p241=p2

14. Solve for pp: -(-16-p)=13p-1-(-16-p)=13p-1

15. Solve for pp: 6p-2+2p=-2+4p+86p-2+2p=-2+4p+8

16. Solve for ff: 3f-10=103f-10=10

17. Solve for ff: 3f+16=4f-103f+16=4f-10

18. Solve for ff: 10f+5+0=-2f+-3f+8010f+5+0=-2f+-3f+80

19. Solve for ff: 8(f-4)=5(f-4)8(f-4)=5(f-4)

20. Solve for ff: 6=6(f+7)+5f6=6(f+7)+5f


## Content actions

PDF | EPUB (?)

### What is an EPUB file?

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

PDF | EPUB (?)

### What is an EPUB file?

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

#### 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?

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?

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

### Reuse / Edit:

Reuse or edit collection (?)

#### Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

#### Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.

| Reuse or edit module (?)

#### Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

#### Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.