3x + 2 -6x =8 +3(x + 2) 3(x +2) =3x +6 then combine each matching similar terms in each equation. 2 -3x = 3x +14... I would first 2 -3x +3x = 3x + 3x =14 = 2 = 6x +14 = 2-14 = 6x +14 -14 = -12 = 6x = -12/-12 6x/-12 the aswer is -2 what didnt I do right this time. could I turn 6x/ -12 into ,like an improper frac. 6x/-12 = -2
i would like to say first of all that the manner in which you post is confusing, please fix it.Originally Posted by Leona_Marie
3x + 2 -6x =8 +3(x + 2) 3(x +2) =3x +6 then combine each matching similar terms in each equation. 2 -3x = 3x +14... I would first 2 -3x +3x = 3x + 3x =14 = 2 = 6x +14 = 2-14 = 6x +14 -14 = -12 = 6x = -12/-12 6x/-12 the aswer is -2 what didnt I do right this time
i suppose you started with 3x + 2 - 6x = 8 + 3(x + 2) .........(you should have started a new line here, you made it look like you were multiplying by 3(x + 2), do you see that?)
anyway, we get
2 - 3x = 8 + 3x + 6 ..............expanded the brackets on the right
=> 2 - 3x = 14 + 3x .............simplified both sides
=> 2 - 14 = 3x + 3x .............added 3x - 14 to both sides
=> -12 = 6x .......................simplified both sides
=> x = -2 ..........................divide both sides by 6
the first thing to do is expand the bracket, collect like terms by moving to different sides of the equation, but when doing so remember to change the sign from negative to positive or positive to negative!
$\displaystyle 3x + 2 -6x =8 +3(x + 2)$
$\displaystyle 3x + 2-6x=8+3x+6$
$\displaystyle 3x-3x-6x=8+6-2$
$\displaystyle -6x=12$
$\displaystyle x=12/-6$
$\displaystyle x=-2$
I think what we both did was the same. I normally dont write it out like that but I wanted to make sure everyone knew what I was doing. when you say simplfy both sides by 6 It makes more sense to me , but I was never taught that way. I was taught like fractions. if your multipling the you divide to simplify. -12/-12 divided by 6x/-12 could you clarify.
i never said "simplify both sides by 6"
what do you need clarification with, there was no real need for writing fractions here, we could add a few steps, but that's it. is this better?
2 - 3x = 8 + 3x + 6 ..............expanded the brackets on the right
=> 2 - 3x = 14 + 3x .............simplified both sides
=> 2 - 14 = 3x + 3x .............added 3x - 14 to both sides
=> -12 = 6x .......................simplified both sides
=> -12/6 = 6x/6 .................divide both sides by 6
=> -2 = x ..........................simplified
i don't really see what to change to clarify, if you have problems with a line, point it out and ask about it.
i honestly don't know what you are doing here, but if you end up with -12 = 6, it's wrong. i usually don't like to force things on people, but do as i did, and forget whatever you're thinking about
the idea is we want to get x by itself. so first, we get all the x's on one side and then combine them. now we want to get rid of everything that is not an x from that side. we do this by performing the opposite operations these things have. example, if something is being added to the x-term, we would subtract it from both sides (example: $\displaystyle x + 2 = 3 \implies x + 2 ~{\color{red}- 2} = 3 ~{\color{red}- 2} \implies x = 1$). if something is multiplying the x-term, we would divide both sides by it (example: $\displaystyle 3x = 9 \implies \frac {3x}{{\color{red}3}} = \frac 9{~{\color{red}3}} \implies x = 3$), etc
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