a) -2/5 + 4/5 : x = 3/5

To solve for x, we can start by simplifying the equation:

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

First, let's simplify the division:

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

Next, let's multiply both sides of the equation by x to eliminate the fraction:

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

Simplifying further:

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

Now, let's combine like terms:

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

To eliminate the fraction, we can multiply both sides of the equation by 5:

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

Simplifying further:

-2x + 4 = 3x

Now, let's isolate x by moving all the terms with x to one side of the equation:

-2x - 3x = -4

Combining like terms:

-5x = -4

Finally, divide both sides of the equation by -5 to solve for x:

x = -4 / -5

Simplifying the fraction:

x = 4/5

Therefore, the value of x that satisfies the equation is x = 4/5.

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

To solve for x, we can follow a similar process as in part a:

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

First, let's simplify the division:

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

Next, let's multiply both sides of the equation by x to eliminate the fraction:

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

Simplifying further:

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

Now, let's combine like terms:

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

To eliminate the fraction, we can multiply both sides of the equation by 7:

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

Simplifying further:

-3x - 4 = -14x

Now, let's isolate x by moving all the terms with x to one side of the equation:

-3x + 14x = -4

Combining like terms:

11x = -4

Finally, divide both sides of the equation by 11 to solve for x:

x = -4 / 11

Therefore, the value of x that satisfies the equation is x = -4/11.