We are asked to calculate the value of the expression: $-1\frac{2}{7} + \frac{3}{7} - \frac{4}{7}$.

1. Problem Description

We are asked to calculate the value of the expression: $-1\frac{2}{7} + \frac{3}{7} - \frac{4}{7}$.

2. Solution Steps

First, convert the mixed number $-1\frac{2}{7}$ to an improper fraction:

$-1\frac{2}{7} = -\frac{(1 \times 7) + 2}{7} = -\frac{7 + 2}{7} = -\frac{9}{7}$

Now we can rewrite the expression as:

$-\frac{9}{7} + \frac{3}{7} - \frac{4}{7}$

Since all fractions have the same denominator, we can combine the numerators:

$\frac{-9 + 3 - 4}{7}$

Calculate the numerator:

$-9 + 3 - 4 = -6 - 4 = -10$

So the expression becomes:

$\frac{-10}{7}$

Which can also be expressed as:

$-\frac{10}{7}$

Converting the improper fraction to a mixed number:

$-\frac{10}{7} = -1\frac{3}{7}$

3. Final Answer

$-1\frac{3}{7}$