How does one simplify...?

1/6 y + 1/12 y = 14/4
add common terms
1/4 y = 14 / 4
get the common factor of both sides of the equation
1/4 ( y ) = 1/4 ( 14 )
divided both sides with that common factor
y = 14

Multiply the first equation by the LCD, which is 12
it yields 2y+y=42
3y=42
y=14

2y + y = 42
3y = 42
y = 14

4x + 24x = 24
28x = 24
x = 24/28
x = 6/7

1)
y/6 + y/12 = 14/4
12(y/6 + y/12) = 12(7/2)
2y + y = 42
3y = 42
y = 42/3
y = 14

2)
x/9 + 2x/3 = 8/12
9(x/9 + 2x/3) = 9(2/3)
x + 6x = 6
7x = 6
x = 6/7

hi
(2y+y)/12=14/4
3y/12=14/4
y/4=14/4
y=14

the second one has fractions so i'll do that one

x/9 + 2x/3 = 8/12
you have to get a lowest common denominator in order to add fractions. so multiply 2x/3 by 3/3 and you get 6x/9.

x/9 + 6x/9 = 8/12
7x/9 = 8/12
this is where you can cross multiply to get x

(7x)(12) = (8)(9)
84x = 72

divide both sides by 84 to solve for x

x= 72/84
both can be divided by 12 so simplify

x = 6/7

You need to get the denomenators of both fractions on the left hand side equal so that you can convert them into one fraction.

y/6 = 2y/12 (you can mjultiply top and bottom of a fraction by the same number - in this case 2)

2y/12 + y/12 = 14/4

(2y + y)/12 = 14/4 (when adding 2 fractions with the same numerators you simply add the tops and keep the same denomenators)

3y/12 = 14/4
3y = (14 x 12)/4 (multiply both sides by 12)
3y = 42
y = 14

hope that helps

y/6+y/12=14/4
=>2y/12+y/12=14/4
=>4{3y}=14*12
=>12y=14*12
=>y=14