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# Variables On Both Sides

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Algebra 1 - solving equations with the variable on both sides

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• Getting prepared to help my 7th Grader with Pre-Algebra homework this year - this slide show was a great help thank you x

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• To guest5de708 - there are no errors in the equations in this slideshow. You should double-check your calculations before leaving a comment like that.

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• There are no errors in the equations in this slide show. Guest5de708 is mistaken. When you add 30 to -60, the result IS -30.

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• wait, u hav a lot of errors in this slide show. nvm. this isnt a good slide show.

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• 1 thing im confused about- in the problem -30 + 25n= 20n - 60, i thot u would do plus thirty to -60, but u added -30 it looks like. can u shed some lite on the situation?

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### Variables On Both Sides

1. 1. 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
2. 2. What you have learned so far (about solving equations) <ul><li>How to solve an equation in one step by addition or subtraction </li></ul><ul><li>How to solve an equation in one step by multiplication or division </li></ul><ul><li>How to solve an equation in two or more steps by all methods listed above </li></ul>
3. 3. What else do you need to know about equations ??? <ul><li>A whole bunch !!! </li></ul>
4. 4. The rules ar e s till the same ….. <ul><li>Solve: 12x + 21 = 9x </li></ul><ul><li>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….. </li></ul><ul><li>12x + 21 = 9x </li></ul><ul><li> - 12x -12x </li></ul><ul><li>21 = - 3x </li></ul><ul><li>Now you have a one step equation to solve: divide both sides by – 3: </li></ul><ul><li> 21 = - 3x </li></ul><ul><li> - 3 - 3 </li></ul><ul><li>-7 = x </li></ul>
5. 5. Let’s try an other one! <ul><li>4n = -28n – 3 </li></ul><ul><li>This time, the variable on the LEFT needs to move…. </li></ul><ul><li>4n = - 28n – 32 </li></ul><ul><li>+28n +28n </li></ul><ul><li>32n = - 32 </li></ul><ul><li>Divide both sides by 32: </li></ul><ul><li>32n = - 32 </li></ul><ul><li> 32 32 </li></ul><ul><li>n = - 1 </li></ul>
6. 6. A little bit harder ….. <ul><li>8a - 4(-5a - 2) = 12a 1 st , do the distributive property to get rid of the parentheses: </li></ul><ul><li>8a + 20a + 8 = 12a </li></ul><ul><li>Add like terms on each side: </li></ul><ul><li>28a + 8 = 12a </li></ul><ul><li>Now it looks like the other ones that we have solved!! </li></ul>
7. 7. <ul><li>To solve for a, now you need to subtract 28a from each side: </li></ul><ul><li>28a + 8 = 12a </li></ul><ul><li> -28a -28a </li></ul><ul><li>8 = -16a </li></ul><ul><li>And solve as usual! (divide both sides by what???) </li></ul><ul><li>8 = -16a </li></ul><ul><li> -16 -16 </li></ul><ul><li>-1/2 = a </li></ul>
8. 8. T ry t hi s one ! <ul><li>– 5(6 - 5n) = 10(2n - 6) </li></ul><ul><li>What would you do FIRST ?? </li></ul>
9. 9. I f y ou s aid t he D istributive P roperty …. Yo u’ re Ri gh t!!
10. 10. Here’s how it should look: <ul><li>– 5(6 - 5n) = 10(2n - 6) </li></ul><ul><li>-30 + 25n = 20n – 60 </li></ul><ul><li>Now, you have to move the variables together on one side, and the numbers without variables to the other side! </li></ul><ul><li>First, you could add 30 to each side…… </li></ul>
11. 11. <ul><li>-30 + 25n = 20n – 60 </li></ul><ul><li>+30 +30 </li></ul><ul><li>Make sure you only add or subtract numbers with other numbers, and letters with other letters (like terms): Now we have </li></ul><ul><li>25n = 20n – 30 </li></ul><ul><li>Subtract: -20n -20n - 30 </li></ul><ul><li>Now we have 5n = -30 </li></ul><ul><li>Divide both sides by 5, to get n = - 6 </li></ul>
12. 12. Pretty Easy, huh? (just kidding!) <ul><li>OK, here’s another one to try: </li></ul><ul><li>½(12n - 4) = 14 - 10n </li></ul><ul><li>( Without any help from me!! ) </li></ul>
13. 13. How did you do? <ul><li>½(12n - 4) = 14 – 10n </li></ul><ul><li>6n - 2 = 14 – 10n </li></ul><ul><li>+10n + 10n </li></ul><ul><li>16n - 2 = 14 </li></ul><ul><li>+ 2 +2 </li></ul><ul><li>16n = 16 </li></ul><ul><li>16 16 </li></ul><ul><li>n = 1 </li></ul>
14. 14. One more thing….. <ul><li>When you are working these problems….it is possible to end up with a FALSE statement: such as-- </li></ul><ul><li>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: </li></ul><ul><li>NO SOLUTION! </li></ul><ul><li>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 !! </li></ul>
15. 15. Your Assignment: <ul><li>P a g e 1 5 2 </li></ul><ul><li>16 – 42 even </li></ul><ul><li>*43, *47 (show work for credit!) </li></ul><ul><li>If you are a Pioneer, and you will miss Thursday, </li></ul><ul><li>then it is HOMEWORK! </li></ul>
16. 16. If you are NOT a Pioneer…. <ul><li>Whatever you do not finish in class today can be worked on during class on Thursday! </li></ul>
17. 17. T h e E n d !