To solve the equation (1/2x + 3) = 8/125, we can start by isolating the variable x.

First, let's subtract 3 from both sides of the equation:
(1/2x + 3) - 3 = 8/125 - 3
1/2x = 8/125 - 375/125
1/2x = -367/125

Next, let's multiply both sides of the equation by 2 to get rid of the fraction:
2 * (1/2x) = 2 * (-367/125)
x = -734/125

Therefore, the solution to the equation (1/2x + 3) = 8/125 is x = -734/125.

Now, let's solve the equation 8/5x - 4/3x = 5/16x * 7/5.

First, let's simplify the equation on the right side:
5/16x * 7/5 = (5 * 7)/(16 * 5) * x
= 35/80x
= 7/16x

Now, let's rewrite the equation:
8/5x - 4/3x = 7/16x

To combine the fractions on the left side, we need to find a common denominator. The least common multiple of 5, 3, and 16 is 240. So, let's rewrite the equation with the common denominator of 240:

(8 * 48)/(5 * 48)x - (4 * 80)/(3 * 80)x = (7 * 15)/(16 * 15)x
384/240x - 320/240x = 105/240x

Now, let's combine the fractions on the left side:
(384 - 320)/240x = 105/240x
64/240x = 105/240x

Since the denominators are the same, we can equate the numerators:
64 = 105

However, 64 is not equal to 105. Therefore, there is no solution to the equation 8/5x - 4/3x = 5/16x * 7/5.