Fractions?

Question

i don't know what to do. Please help.

1/3(6y - 9) = -2y + 13

1/6(12 - 6x) = 5(x + 4)

Answer 1

use distribute property
2y-3= -2y+13
add 2y
4y-3=13
add 3
4y=16
y=4

2-x=5x+20
add x
2=6x+20
subtract 20
-18=6x
divided 6
x= -3

Answer 2

You have two independent questions and not a system as a such.

So you can separately solve the equations:
since they are equations you multiply, sum at both sides of the equation. I mean, it holds the "=" sign.
For fractions you multiply if it is divided by.
So if Divided by 3, Then you Multiply by 3.
3 * [ ( 6y - 9 ) / 3 = -2y + 13 ] ==>
6y - 9 = 3 (-2y + 13) ==>
6y - 9 = -6y + 39

You add +6y at both sides,
6y - 9 + 6y = -6y + 39 + 6y ==>
6y - 9 + 6y = (-6 + 6)y + 39 ==>
12y - 9 = 0y + 39 ==>

Since all number multiply for cero is cero.
0y = 0
And Since 0 is neutral/identity element in addition
0y + 39 = 39

However, we must isolate the y. For this aim, we add
both side of the equation with +9. So "12y" will stay alone
on the left-side of the equation.
12y -9 = 39 ==>
12y -9 +9 = 39 +9 ==>
12y + 0 = 48 ==>
12y = 48 ==>
Now, we divide both sides by 12 as ever to leave the
x-variable alone.
12y /12 = 48 /12 ==>
1y = 4 ==>
y = 4

Finally, we proove it as follows (if y = 4, the equation):
(6*4 - 9)/3 = -2*(4) + 13 ==>
( 24 - 9 ) / 3 = -8 +13 ==>
15 / 3 = 5 ==>
5 = 5

It's alright...!!!
C'est correct...!!!
Esta Correcta...!!!

The other equation must be solved and prooved like this.
Practice it. However, the answer is:

1/6(12 - 6x) = 6/6(2-x) = 2 -x
2 - x = 5x + 20
-20 + 2 = 5x + x
-18 = 6x
x = -18/6 = -3


OR THE LONG WAY:
6* [1/6(12 - 6x) = 5(x + 4)] ==>
12 - 6x = 30( x + 4) ==>
12 - 6x = 30x + 120 ==>
12 - 6x -30x -12 = 30x + 120 -30x -12 ==>
-36x + 0 = 120 - 12 = 108 ==>
[ -36x + 0 = 120 - 12 = 108 ] /(-36) ==>
x = 108 / (-36) = -3 ==>
x = -3

Prove it.

Answer 3

1/3(6y - 9) = -2y + 13
(6y - 9) = (-2y + 13)*3
6y - 9 = -6y + 39
6y - 9 + 6y = -6y + 39 + 6y
12y - 9 = 39
12y - 9 + 9 = 39 + 9
12y = 48
12y/12 = 48/12
y = 4


1/6(12 - 6x) = 5(x + 4)
1/6(12 - 6x) = 5x + 20
1/6(12 - 6x) * 6 = (5x + 20) * 6
12 - 6x = 30x + 120
12 - 6x + 6x= 30x + 120 + 6x
12 = 36x + 120
12 - 120 = 36x + 120 - 120
-108 = 36x
-108/36 = 36x/36
-3 = x

Answer 4

1)1/3(6y - 9) = -2y + 13
2y-3= -2y+13
4y =16
y =16/4
y =4

2)1/6(12 - 6x) = 5(x + 4)
2-x =5x=20
-18=6x
-18/6=x
-3=x
DAM U R LUCKY I WISH I HAD SOM1 TO DO MY HOMEWORK........LOL

Answer 5

multiply through ...
(1/3)6y - (1/3)9) = 2Y +13
(6/3)y - (9/3) = -2Y+13
2Y - 3 = -2y + 13 ....
2Y (+2Y) (+3) = -2Y (+2y) (+3) +13
4Y = 16
y = 4


(12/6) - (6/6)x = 5*X + (5*4)
2 - X = 5x + 20
2 (+X) -20 = 5X (+X) -20 [minus 20 & X cancel on each side]
2 -20 = 6X
-18 = 6X
(-18/6) = (6/6)X
-3 = X

Answer 6

1) y = 4
2)x = -3

Answer 7

if these are two different problems, the first one multiply both sides by 3 (to cancel the fraction out and then solve for y.

the second one you multiply by 6, and then solve for x.