a) To solve for x, we can start by subtracting 5/7 from both sides of the equation:

2/5 x = 3/10 - 5/7

Next, we need to find a common denominator for 10 and 7, which is 70. We can rewrite the fractions with this common denominator:

2/5 x = (3/10)(7/7) - (5/7)(10/10)
2/5 x = 21/70 - 50/70

Now, we can subtract the fractions:

2/5 x = -29/70

To isolate x, we can multiply both sides of the equation by the reciprocal of 2/5, which is 5/2:

x = (-29/70)(5/2)
x = -145/140
x = -1.036

b) To solve for x, we can start by adding 1/2 to both sides of the equation:

3/4 x = 3/7 + 1/2

Next, we need to find a common denominator for 7 and 2, which is 14. We can rewrite the fractions with this common denominator:

3/4 x = (3/7)(2/2) + (1/2)(7/7)
3/4 x = 6/14 + 7/14

Now, we can add the fractions:

3/4 x = 13/14

To isolate x, we can multiply both sides of the equation by the reciprocal of 3/4, which is 4/3:

x = (13/14)(4/3)
x = 52/42
x = 1.238

c) To solve for x, we can start by subtracting -2/5 from both sides of the equation:

5/6 x = -4/15 - (-2/5)

Next, we need to simplify the expression on the right side:

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

To find a common denominator for 15 and 5, we can multiply 15 by 3 and 5 by 3:

5/6 x = -4/15 + 6/15

Now, we can add the fractions:

5/6 x = 2/15

To isolate x, we can multiply both sides of the equation by the reciprocal of 5/6, which is 6/5:

x = (2/15)(6/5)
x = 12/75
x = 0.16

d) To solve for x, we can start by adding 4/5 to both sides of the equation:

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

Next, we need to find a common denominator for 10 and 5, which is 10. We can rewrite the fractions with this common denominator:

5/2 x = (-3/10)(1/1) + (4/5)(2/2)
5/2 x = -3/10 + 8/10

Now, we can add the fractions:

5/2 x = 5/10

To simplify the expression on the right side, we can divide both the numerator and denominator by 5:

5/2 x = 1/2

To isolate x, we can multiply both sides of the equation by the reciprocal of 5/2, which is 2/5:

x = (1/2)(2/5)
x = 2/10
x = 0.2