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Linear Equations

Linear Equations

- Solving linear equations
- Whatever you do to one side of an equation, you

must also do to the other. - Goal is to get the variable alone on one side of

the equation by undoing the listed operations.

Linear Equations

- Examples
- X 4 8
- 4 4 subtract 4 (or add 4) to

both sides - X 4
- To check substitute your solution for the

variable and see if the statement is true. - X 4 8, X 4 therefore
- 4 4 8 (true)

Linear Equations

- 4x 48
- 4 4 since 4 is multiplying x we

divide both - sides by 4 to make the

coefficient of x 1 - x 12
- Simplify first to get only one term with the

variable! - 2x 3x 13 2
- 5x 15 simplify by combining

like terms - 5 5 divide both sides by 5
- x 3

Linear Equations

- Two operations
- 2x 4 8 nothing to simplify
- 4 4 subtract 4 from both sides
- 2x 4
- 2 2 divide both sides by 2
- x 2

Linear Equations

- Variables on both sides of equation
- 9 4x 8x cant simplify since 4x and 8x are
- on opposite sides of the equation. Remember

the goal is to get one term with the variable! - 9 4x 8x
- 4x 4x add 4x to both sides to

get the x - terms together
- 9 12x
- 12 12 divide both sides by 12
- ¾ x

Linear Equations

- Variables on both sides (2 methods)
- 9x 2 6x 10 Method 1 move constants first
- 2 2 Subtract 2 from both

sides - 9x 6x 12
- 6x 6x subtract 6x from both sides
- 3x 12
- 3 3 divide both sides by 3
- x 4

Linear Equations

- Variables on both sides (2 methods)
- 9x 2 6x 10 Method 2 move variables

first - 6x 6x subtract 6x from both

sides - 3x 2 10
- 2 2 subtract 2 from both

sides - 3x 12
- 3 3 divide both sides

by 3 - x 4

Linear Equations

- Applying the Distributive Property
- 28 7x 3(x 4)
- 28 7x ( 3)x ( 4) change subtract to

add opp. - 28 7x ( 3x) 12 distribute the 3 to

all terms - 28 4x 12 simplify
- 12 12 subtract 12

from both sides - 16 4x
- 4 4 divide both

sides by 4 - 4 x

Linear Equations

- Applying the Distributive Property
- 6 ( x 3 ) 2x think of the before the

parenthesis as a 1 - 6 1(x 3) 2x
- 6 1x 3 2x distribute the 1 thru the

parenthesis - 3 1x 2x simplify
- 1x 1x add 1x to both sides
- 3 3x
- 3 3 divide both sides by 3
- 1 x

Linear Equations

- Special cases (1)
- 4x 3 3x 3 x
- 4x 3 4x 3 simplify
- 4x 4x subtract 4x from both sides
- 3 3
- Since 3 DOES equal 3, we say that ALL real

numbers are solutions!

Linear Equations

- Special cases (2)
- 3x 7 x 2x 11
- 3x 7 3x 11 simplify
- 3x 3x subtract 3x from both sides
- 7 11
- Since 7 DOES NOT equal 11, we say that there

is NO solution to this equation. In other words,

no real number will make this equation true!

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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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