1) To solve this equation, we can start by simplifying both sides:

2(1/4 - 3x) = 1/5 - 4x

First, distribute the 2 on the left side:

1/2 - 6x = 1/5 - 4x

Next, combine like terms on both sides:

-6x + 4x = 1/5 - 1/2

-2x = 1/5 - 2/10

-2x = 1/5 - 1/5

-2x = 0

Finally, divide both sides by -2 to solve for x:

x = 0

So the solution to the equation is x = 0.

2) To solve this equation, we can start by simplifying both sides:

5/2 - 3(1/3 - x) = 1/4 - 7x

First, distribute the 3 on the left side:

5/2 - 1 + 3x = 1/4 - 7x

Next, combine like terms on both sides:

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

Next, add 7x to both sides:

10x - 1/2 = 1/4

Next, add 1/2 to both sides:

10x = 1/4 + 1/2

10x = 1/4 + 2/4

10x = 3/4

Finally, divide both sides by 10 to solve for x:

x = 3/40

So the solution to the equation is x = 3/40.

3) To solve this equation, we can start by simplifying both sides:

4(1/3 - x) + 1/2 = 5/6 + x

First, distribute the 4 on the left side:

4/3 - 4x + 1/2 = 5/6 + x

Next, combine like terms on both sides:

-4x + x = 5/6 - 4/3 - 1/2

-3x = 5/6 - 8/6 - 3/6

-3x = -6/6

-3x = -1

Finally, divide both sides by -3 to solve for x:

x = 1/3

So the solution to the equation is x = 1/3.

4) To solve this equation, we can start by simplifying both sides:

3(1/2 - x) - 5(x - 1/10) = -7/4

First, distribute the 3 and -5 on the left side:

3/2 - 3x - 5x + 1/2 = -7/4

Next, combine like terms on both sides:

-8x + 2 = -7/4 - 3/2

-8x + 2 = -7/4 - 6/4

-8x + 2 = -13/4

Next, subtract 2 from both sides:

-8x = -13/4 - 8/4

-8x = -21/4

Finally, divide both sides by -8 to solve for x:

x = 21/32

So the solution to the equation is x = 21/32.

5) To solve this equation, we can start by simplifying both sides:

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

First, simplify the expression inside the parentheses on the left side:

1/2(8/10 - 15/10) + x = 5(x - 1/10)

1/2(-7/10) + x = 5(x - 1/10)

Next, multiply 1/2 by -7/10:

-7/20 + x = 5(x - 1/10)

Next, distribute the 5 on the right side:

-7/20 + x = 5x - 5/2

Next, subtract x from both sides:

-7/20 = 4x - 5/2

Next, add 5/2 to both sides:

-7/20 + 5/2 = 4x

Next, find a common denominator for -7/20 and 5/2:

-7/20 + 50/20 = 4x

43/20 = 4x

Finally, divide both sides by 4 to solve for x:

x = 43/80

So the solution to the equation is x = 43/80.

6) To solve this equation, we can start by simplifying both sides:

4(3/4 + x) - 1/5 = 7x - 1/7

First, distribute the 4 on the left side:

3 + 4x - 1/5 = 7x - 1/7

Next, combine like terms on both sides:

4x - 1/5 - 7x = -3 + 1/7

-3x - 1/5 = -21/7 + 1/7

-3x - 1/5 = -20/7

Next, find a common denominator for -1/5 and -20/7:

-3x - 7/35 = -100/35

Next, add 7/35 to both sides:

-3x = -100/35 + 7/35

-3x = -93/35

Finally, divide both sides by -3 to solve for x:

x = 31/105

So the solution to the equation is x = 31/105.