To solve each of these equations for the respective variables, we will isolate them one by one.
1) 3/5 + x = 4/5y - 2/7
First, let's isolate x by subtracting 3/5 from both sides:x = 4/5y - 2/7 - 3/5x = 4/5y - 2/7 - 9/35x = 4/5y - (10/35 + 9/35)x = 4/5y - 19/35
2) 7/25 - k = 7/25d + 2/9
To isolate k, we will subtract 7/25d and 2/9 from both sides:-k = 7/25d + 2/9 - 7/25-k = 7/25d + 2/9 - 7/25-k = 7/25d + (2/9 - 7/25)-k = 7/25d + (10/45 - 21/45)-k = 7/25d - 11/45k = -7/25d + 11/45
3) 1/9 + 7/9 = 3/5d + 2/9
To isolate d, we will first combine the fractions on the left side:8/9 = 3/5d + 2/9
Next, subtract 2/9 from both sides to isolate 3/5d:8/9 - 2/9 = 3/5d6/9 = 3/5d2/3 = 3/5d
Now, divide both sides by 3/5 to solve for d:d = (2/3) / (3/5)d = (2/3) * (5/3)d = 10/9
Therefore, the solutions to the equations are:1) x = 4/5y - 19/352) k = -7/25d + 11/453) d = 10/9
To solve each of these equations for the respective variables, we will isolate them one by one.
1) 3/5 + x = 4/5y - 2/7
First, let's isolate x by subtracting 3/5 from both sides:
x = 4/5y - 2/7 - 3/5
x = 4/5y - 2/7 - 9/35
x = 4/5y - (10/35 + 9/35)
x = 4/5y - 19/35
2) 7/25 - k = 7/25d + 2/9
To isolate k, we will subtract 7/25d and 2/9 from both sides:
-k = 7/25d + 2/9 - 7/25
-k = 7/25d + 2/9 - 7/25
-k = 7/25d + (2/9 - 7/25)
-k = 7/25d + (10/45 - 21/45)
-k = 7/25d - 11/45
k = -7/25d + 11/45
3) 1/9 + 7/9 = 3/5d + 2/9
To isolate d, we will first combine the fractions on the left side:
8/9 = 3/5d + 2/9
Next, subtract 2/9 from both sides to isolate 3/5d:
8/9 - 2/9 = 3/5d
6/9 = 3/5d
2/3 = 3/5d
Now, divide both sides by 3/5 to solve for d:
d = (2/3) / (3/5)
d = (2/3) * (5/3)
d = 10/9
Therefore, the solutions to the equations are:
1) x = 4/5y - 19/35
2) k = -7/25d + 11/45
3) d = 10/9