To solve the equation, we need to isolate the variable x.

Given: -4/7 - x = 3/5 - 2x

First, let's simplify both sides of the equation:

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

To combine the fractions on the right side, we need to find a common denominator. The least common multiple of 7 and 5 is 35.

-4/7 - x = (3/5) * (7/7) - (2x) * (7/7)
-4/7 - x = 21/35 - 14x/35

Now, let's combine the fractions on the right side:

-4/7 - x = (21 - 14x)/35

To eliminate the fractions, we can multiply both sides of the equation by 35:

35 * (-4/7 - x) = 35 * (21 - 14x)/35

Simplifying further:

-20 - 35x = 21 - 14x

Next, let's isolate the x terms on one side and the constant terms on the other side:

-35x + 14x = 21 + 20

Simplifying further:

-21x = 41

Now, divide both sides of the equation by -21 to solve for x:

-21x / -21 = 41 / -21

Simplifying further:

x = -41/21

Therefore, the solution to the equation is x = -41/21.