SOLUTION: how can i solve this equation 1/4(x-3)+5/6=7/12x+2/3 this is what I have but is wrong. 1/4(x-3)+5/6=7/12x+2/3 3(3x-36)+10=7x+8

Question 316855: how can i solve this equation 1/4(x-3)+5/6=7/12x+2/3
this is what I have but is wrong. 1/4(x-3)+5/6=7/12x+2/3
3(3x-36)+10=7x+8
9x-108+10=7x+8
-7 -7
2x-108+10=8
-8 -8
2x=-106+2-108
2x/2=-106/2
x=-53

Found 2 solutions by Theo, mananth:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
It looks like your equation is:

Multiply both sides of this equation by 12 to get:

Use the distributive law of multiplication to get:

Simplify this to get:

Use the distributive law of multiplication again to get:

Simplify this by combining like terms to get:

Subtract 3*x from both sides of this equation and subtract 8 from both sides of this equation to get:

this is the same as

Divide both sides of this equation by 4 to get:

If the answer is correct, you should be able to substitute for x in the original equation and confirm that the equation is true.

The original equation is:

When x = (-7/4), this equation becomes:

I used my calculator to solve and I got:

-.354166667 = -.354166667 which confirms that that value of x = -7/4 is good.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
1/4(x-3)+5/6=7/12x+2/3
1/4(x-3)-7/12x=-5/6+2/3
LCM = 12x(x-3)
3x-7(x-3) / 12x(x-3)= -5+4 / 6
..
3x-7x+21 / 12x(x-3) = -1/6
..
6(3x-7x+21) = -12(x-3)
..
18x-42x+126 = -12x+36
18x+12x -42x=+36-126
-12x=-90
x= 7.5
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