SOLUTION: 1/3(x-7)+5=6x+4 1/3x-7/3+5=6x+4 1/3x=6x+34/3 -17/3x=34/3 -102/51 x=-2 is this correct?

Question 557047: 1/3(x-7)+5=6x+4
1/3x-7/3+5=6x+4
1/3x=6x+34/3
-17/3x=34/3
-102/51
x=-2
is this correct?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i get x = -4/17
if i replace x in the original equation with -4/17, then i get:
1/3(x-7)+5=6x+4 becomes:
(1/3)*((-4/17)-7) + 5 = 6(-4/17) + 4
since am just confirming, i use my calculator to simplify this equation to:
2.588235294 = 2.588235294
this confirms the solution of x = (-4/17) is good.
looking at what you did, you were good up until:
1/3x-7/3+5=6x+4
your next statement looks like where you went wrong.
that statement is:
1/3x=6x+34/3
starting from your last good statement of:
1/3x-7/3+5=6x+4
you want to add 7/3 to both sides of the equation and you want to subtract 5 from both sides of the equation to get:
(1/3)x = 6x + 4 + 7/3 - 5
you can combine like terms to make this:
(1/3)x = 6x - 1 + 7/3
since -1 is equivalent to -3/3, you can combine like terms again to make this:
(1/3)x = 6x -3/3 + 7/3 which becomes:
(1/3)x = 6x + 4/3 ******* see note 1 below.
you now want to get all the x's over to the left side of the equation.
you do this by subtracting 6x from both sides of the equation to get:
(1/3)x - 6x = 4/3
since -6 is equivalent to -18, you can simplify this equation to become:
(1/3)x - (18/3)x = 4/3
you can now combine like terms to get:
(-17/3)x = 4/3
if you multiply both sides of this equation by -3/17), then you will get:
x = (4/3) * (-3/17) which you can simplify to:
x = (-12/51) which can be further simplified to:
x = (-4/17)
***** note 1:
this is where you went wrong.
you wound up with (1/3)x = 6x + 34/3
i wound up with (1/3)x = 6x + 4/3
i'm not sure what you did different, but see what i did and then see what you did that was different from that.

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