1) To solve for x, we can multiply both sides of the equation by the reciprocal of -7, which is -1/7:

(-7)x = 1/49
(-1/7)(-7)x = (-1/7)(1/49)
x = -1/343

Therefore, x = -1/343.

2) To solve for x, we can divide both sides of the equation by -10:

(-10)x = -1/10
(-10)x / -10 = (-1/10) / -10
x = 1/100

Therefore, x = 1/100.

3) To solve for x, we can multiply both sides of the equation by the reciprocal of 1/2, which is 2:

(1/2)x = 1/32
(2)(1/2)x = (2)(1/32)
x = 1/64

Therefore, x = 1/64.

4) To solve for x, we can multiply both sides of the equation by the reciprocal of 7/5, which is 5/7:

343/125 = (7/5)x
(5/7)(343/125) = (5/7)(7/5)x
x = 49/25

Therefore, x = 49/25.

5) To solve for x, we can divide both sides of the equation by -2:

(-2)x = -0.5
(-2)x / -2 = (-0.5) / -2
x = 0.25

Therefore, x = 0.25.

6) To solve for x, we can divide both sides of the equation by -2:

(-2)x = -0.125
(-2)x / -2 = (-0.125) / -2
x = 0.0625

Therefore, x = 0.0625.