Final answer:
The equation provided simplifies to a contradiction with no x variable remaining, suggesting either a mistake in the original equation or that there is no solution for x.
Step-by-step explanation:
To solve the equation x + frac{2}{5} - x - frac{2}{3} = -4, we first combine like terms and manage the fractions. Since there is an x and a -x, they cancel each other out, so we are left with frac{2}{5} - frac{2}{3} = -4. To combine the fractions, we find a common denominator, which is 15. The equation then becomes frac{6}{15} - frac{10}{15} = -4. Simplifying further, we get -frac{4}{15} = -4. To solve for x, we would normally isolate x, but since x has been eliminated, there is no variable to solve for, which implies either a contradiction or that the original equation was faulty or not written as intended. Hence, there is no solution for x in terms of this equation as provided.