I need help solving this grade 9 math question..someone show me step by step please!1/2(y+2)=y/3?

Question

1/2(y+2)=y/3

the second question:
4x-1/5=2x+3/2

Answer 1

.5y+1 =y/3
1.5y+3=y
3=-.5y
-6=y

2x-.2=1.5
2x=1.7
x=1.7/2

Answer 2

1/2(y+2) = y/3 is ambiguous.
It could be (1/2)(y+2) or
1/(2(y+2))
If it is
(1/2)(y+2) = y/3
multiply through by the LCD
6(1/2)(y+2) = 6y/3
3(y+2) = 2y
3y + 6 = 2y
Subtract 2y from each side
y + 6 = 0
Subtracting 6 from each side
y = - 6

If it is
1/(2(y+2)) = y/3
Multiplying both sides by 3,
3/(2(y+2)) = y
Multiplying both sides by (2(y+2))
3 = 2y(y+2)
3 = 2y^2 + 4y
Swapping sides,
2y^2 + 4y = 3
Subtracting 3 from each side,
2y^2 + 4y - 3 = 0
Dividing everything by 2,
y^2 + 2y - 3/2 = 0
Completing the square,
y^2 + 2y + 1 - 1 - 3/2 = 0
(y + 1)^2 - 5/2 = 0
(y + 1 - √(5/2)(y + 1 + √(5/2) = 0
y = - 1 + (1/2)√10, - 1 - (1/2)√10

4x - 1/5 = 2x + 3/2
Adding 1/5 and subtracting 2x on each side
2x = 3/2 + 1/5
2x = 15/10 + 2/10
2x = 17/10
x = 17/20

Answer 3

Question 1
Assume that question is:-
(1/2).(y + 2) = y / 3
3.(y + 2) = 2y
3y + 6 = 2y
y = - 6

Question 2
Assume question is as written:-
4x - 1/5 = 2x + 3/2
2x = 3/2 + 1/5
2x = 15/10 + 2/10
2x = 17/10
x = 17/20

Answer 4

1) open up the brackets is the first thing to do to solve any question... its makes it easier
since, 1/2 = 0.5 ...
0.5y + 2(0.5) = y/3
3(0.5y) + 6(0.5) = y ..... after multiplying both sides by 3
1.5y + 3 = y
1.5y - y = -3
0.5y = -3
y = -6

2) 4x - 2x = (3/2) + (1/5)
2x = 1.5 + 0.2 ............. taking similar terms on the same side (remember to change the signs while taking it to the other side)
2x = 1.7
x = 1.7/2

Hope this helps!

Answer 5

(y+2)/2=y/3
3y+6=2y
3y-2y=-6
y=-6


4x-1/5=2x+3/2
4x-2x=3/2+1/5
2x=(15+2)/10
x=17/20