Variables On Both Sides

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Information about Variables On Both Sides

Published on October 30, 2007

Author: kdwilliams

Source: slideshare.net

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Algebra 1 - solving equations with the variable on both sides

E q u a t i o n s w i t h t h e V a r i a b l e o n B O T H S I D E S ! ! ! Notes and examples 3-5

What you have learned so far (about solving equations) How to solve an equation in one step by addition or subtraction How to solve an equation in one step by multiplication or division How to solve an equation in two or more steps by all methods listed above

How to solve an equation in one step by addition or subtraction

How to solve an equation in one step by multiplication or division

How to solve an equation in two or more steps by all methods listed above

What else do you need to know about equations ??? A whole bunch !!!

A whole bunch !!!

The rules ar e s till the same ….. Solve: 12x + 21 = 9x You have to get the x’s all on the same side. To do this, you move the 12x AWAY from the side with the 21 by subtracting it from both sides….. 12x + 21 = 9x - 12x -12x 21 = - 3x Now you have a one step equation to solve: divide both sides by – 3: 21 = - 3x - 3 - 3 -7 = x

Solve: 12x + 21 = 9x

You have to get the x’s all on the same side. To do this, you move the 12x AWAY from the side with the 21 by subtracting it from both sides…..

12x + 21 = 9x

- 12x -12x

21 = - 3x

Now you have a one step equation to solve: divide both sides by – 3:

21 = - 3x

- 3 - 3

-7 = x

Let’s try an other one! 4n = -28n – 3 This time, the variable on the LEFT needs to move…. 4n = - 28n – 32 +28n +28n 32n = - 32 Divide both sides by 32: 32n = - 32 32 32 n = - 1

4n = -28n – 3

This time, the variable on the LEFT needs to move….

4n = - 28n – 32

+28n +28n

32n = - 32

Divide both sides by 32:

32n = - 32

32 32

n = - 1

A little bit harder ….. 8a - 4(-5a - 2) = 12a 1 st , do the distributive property to get rid of the parentheses: 8a + 20a + 8 = 12a Add like terms on each side: 28a + 8 = 12a Now it looks like the other ones that we have solved!!

8a - 4(-5a - 2) = 12a 1 st , do the distributive property to get rid of the parentheses:

8a + 20a + 8 = 12a

Add like terms on each side:

28a + 8 = 12a

Now it looks like the other ones that we have solved!!

To solve for a, now you need to subtract 28a from each side: 28a + 8 = 12a -28a -28a 8 = -16a And solve as usual! (divide both sides by what???) 8 = -16a -16 -16 -1/2 = a

To solve for a, now you need to subtract 28a from each side:

28a + 8 = 12a

-28a -28a

8 = -16a

And solve as usual! (divide both sides by what???)

8 = -16a

-16 -16

-1/2 = a

T ry t hi s one ! – 5(6 - 5n) = 10(2n - 6) What would you do FIRST ??

– 5(6 - 5n) = 10(2n - 6)

What would you do FIRST ??

I f y ou s aid t he D istributive P roperty …. Yo u’ re Ri gh t!!

Here’s how it should look: – 5(6 - 5n) = 10(2n - 6) -30 + 25n = 20n – 60 Now, you have to move the variables together on one side, and the numbers without variables to the other side! First, you could add 30 to each side……

– 5(6 - 5n) = 10(2n - 6)

-30 + 25n = 20n – 60

Now, you have to move the variables together on one side, and the numbers without variables to the other side!

First, you could add 30 to each side……

-30 + 25n = 20n – 60 +30 +30 Make sure you only add or subtract numbers with other numbers, and letters with other letters (like terms): Now we have 25n = 20n – 30 Subtract: -20n -20n - 30 Now we have 5n = -30 Divide both sides by 5, to get n = - 6

-30 + 25n = 20n – 60

+30 +30

Make sure you only add or subtract numbers with other numbers, and letters with other letters (like terms): Now we have

25n = 20n – 30

Subtract: -20n -20n - 30

Now we have 5n = -30

Divide both sides by 5, to get n = - 6

Pretty Easy, huh? (just kidding!) OK, here’s another one to try: ½(12n - 4) = 14 - 10n ( Without any help from me!! )

OK, here’s another one to try:

½(12n - 4) = 14 - 10n

( Without any help from me!! )

How did you do? ½(12n - 4) = 14 – 10n 6n - 2 = 14 – 10n +10n + 10n 16n - 2 = 14 + 2 +2 16n = 16 16 16 n = 1

½(12n - 4) = 14 – 10n

6n - 2 = 14 – 10n

+10n + 10n

16n - 2 = 14

+ 2 +2

16n = 16

16 16

n = 1

One more thing….. When you are working these problems….it is possible to end up with a FALSE statement: such as-- 1. The variables cancel each other out, and you are left with just numbers, like 5 = 13, which CAN NOT be true – so the answer is: NO SOLUTION! 2. The numbers cancel each other out and you are left with just variables, like 2x = 3x: which CAN be true, only if x = 0! So your answer for that kind is x = 0 !!

When you are working these problems….it is possible to end up with a FALSE statement: such as--

1. The variables cancel each other out, and you are left with just numbers, like 5 = 13, which CAN NOT be true – so the answer is:

NO SOLUTION!

2. The numbers cancel each other out and you are left with just variables, like 2x = 3x: which CAN be true, only if x = 0! So your answer for that kind is x = 0 !!

Your Assignment: P a g e 1 5 2 16 – 42 even *43, *47 (show work for credit!) If you are a Pioneer, and you will miss Thursday, then it is HOMEWORK!

P a g e 1 5 2

16 – 42 even

*43, *47 (show work for credit!)

If you are a Pioneer, and you will miss Thursday,

then it is HOMEWORK!

If you are NOT a Pioneer…. Whatever you do not finish in class today can be worked on during class on Thursday!

Whatever you do not finish in class today can be worked on during class on Thursday!

T h e E n d !

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