a) To solve the equation 2/5 + x = 2/7, we need to isolate the variable x.

First, let's get rid of the fractions by finding a common denominator. The least common denominator (LCD) for 5 and 7 is 35.

Multiplying both sides of the equation by 35, we get:

(35)(2/5) + (35)(x) = (35)(2/7)
14 + 35x = 10

Next, let's isolate x by subtracting 14 from both sides:

35x = 10 - 14
35x = -4

Finally, divide both sides by 35 to solve for x:

x = -4/35

Therefore, the solution to the equation 2/5 + x = 2/7 is x = -4/35.

b) To solve the equation x + 3/5 = -2/5, we need to isolate the variable x.

First, let's get rid of the fractions by finding a common denominator. The least common denominator (LCD) for 5 and 5 is 5.

Multiplying both sides of the equation by 5, we get:

(5)(x) + (5)(3/5) = (5)(-2/5)
5x + 3 = -2

Next, let's isolate x by subtracting 3 from both sides:

5x = -2 - 3
5x = -5

Finally, divide both sides by 5 to solve for x:

x = -5/5
x = -1

Therefore, the solution to the equation x + 3/5 = -2/5 is x = -1.

c) To solve the equation x - 8/3 = 3/7, we need to isolate the variable x.

First, let's get rid of the fractions by finding a common denominator. The least common denominator (LCD) for 3 and 7 is 21.

Multiplying both sides of the equation by 21, we get:

(21)(x) - (21)(8/3) = (21)(3/7)
21x - 56 = 9

Next, let's isolate x by adding 56 to both sides:

21x = 9 + 56
21x = 65

Finally, divide both sides by 21 to solve for x:

x = 65/21

Therefore, the solution to the equation x - 8/3 = 3/7 is x = 65/21.

d) To solve the equation 3/5 - x = 7/3, we need to isolate the variable x.

First, let's get rid of the fractions by finding a common denominator. The least common denominator (LCD) for 5 and 3 is 15.

Multiplying both sides of the equation by 15, we get:

(15)(3/5) - (15)(x) = (15)(7/3)
9 - 15x = 35

Next, let's isolate x by subtracting 9 from both sides:

-15x = 35 - 9
-15x = 26

Finally, divide both sides by -15 to solve for x:

x = 26/-15
x = -26/15

Therefore, the solution to the equation 3/5 - x = 7/3 is x = -26/15.