SOLUTION: these are some problems my son has in the 7th grade and I don't know how to help him. I have tried many web sites and all I could find are calculators but it does not help him unde

Question 962343: these are some problems my son has in the 7th grade and I don't know how to help him. I have tried many web sites and all I could find are calculators but it does not help him understand the steps. Mostly when are you supposed to to add but really subtract?
2/5 + 3/2y = 1/2
1/2 (4-d) = 2/5
3 (x + 2/9) = 2/3
9/10 + b = 3/4

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) 2/5 + 3/2y = 1/2
b) 1/2 (4-d) = 2/5
c) 3 (x + 2/9) = 2/3
d) 9/10 + b = 3/4
****************************
a) 2/5 + 3/2y = 1/2
subtract 2/5 from both sides of =
3/2y = 1/2 - 2/5
put fractions on right side of = over a common denominator
3/2y = 5/10 - 4/10
3/2y = 1/10
cross multiply the fractions
30 = 2y
y = 15
now substitute for y in original equation to check answer for y
2/5 + 3/ (2*15) = 1/2
2/5 + 3/30 = 1/2
12/30 + 3/30 = 1/2
15/30 = 1/2
1/2 = 1/2
our answer checks
*******************************
b) 1/2 (4-d) = 2/5
multiply both sides of = by 2
4 - d = 4/5
subtract 4 from both sides of =
-d = 4/5 - 4
-d = 4/5 - 20/5
-d = -16/5
d = 16/5
nod substitute for d in original equation to check answer
1/2 (4 - 16/5) = 2/5
1/2 (20/5 - 16/5) = 2/5
1/2 * 4/5 = 2/5
2/5 = 2/5
our answer for y checks
*************************************
c) 3 (x + 2/9) = 2/3
divide both sides of = by 3
x + 2/9 = 2/9
x = 0
substitute for x
3 * (0 + 2/9) = 2/3
6/9 = 2/3
2/3 = 2/3
our answer checks
**************************************
d) 9/10 + b = 3/4
subtract 9/10 from both sides of =
b = 3/4 - 9/10
b = 15/20 - 18/20
b = -3/20
substitute for b
9/10 - 3/20 = 3/4
18/20 - 3/20 = 3/4
15/20 = 3/4
3/4 = 3/4
our answer for y checks

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