To solve each equation for x, we will isolate the variable on one side of the equation.

a) 2/5x + 5/7 = 3/10

First, let's get rid of the fractions by multiplying every term by the least common denominator (LCD), which is 70.

70 * (2/5x) + 70 * (5/7) = 70 * (3/10)

28x + 50 = 21

Next, let's isolate x by subtracting 50 from both sides.

28x = 21 - 50

28x = -29

Finally, divide both sides by 28 to solve for x.

x = -29/28

b) 3/4x - 1/2 = 3/7

To eliminate the fractions, we will multiply every term by the LCD, which is 28.

28 * (3/4x) - 28 * (1/2) = 28 * (3/7)

21x - 14 = 12

Next, let's isolate x by adding 14 to both sides.

21x = 12 + 14

21x = 26

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

x = 26/21

c) -2/5 + 5/6x = -4/15

To eliminate the fractions, we will multiply every term by the LCD, which is 30.

30 * (-2/5) + 30 * (5/6x) = 30 * (-4/15)

-12 + 25x = -8

Next, let's isolate x by adding 12 to both sides.

25x = -8 + 12

25x = 4

Finally, divide both sides by 25 to solve for x.

x = 4/25

d) -4/5 + 5/2x = -3/10

To eliminate the fractions, we will multiply every term by the LCD, which is 10.

10 * (-4/5) + 10 * (5/2x) = 10 * (-3/10)

-8 + 25x = -3

Next, let's isolate x by adding 8 to both sides.

25x = -3 + 8

25x = 5

Finally, divide both sides by 25 to solve for x.

x = 5/25

Simplifying x = 5/25, we get x = 1/5.