The problem asks us to evaluate the expression $ -\frac{4}{7} + 1\frac{3}{7} + 1\frac{2}{7} $.

1. Problem Description

The problem asks us to evaluate the expression $-\frac{4}{7} + 1\frac{3}{7} + 1\frac{2}{7}$.

2. Solution Steps

First, we convert the mixed numbers to improper fractions.

$1\frac{3}{7} = \frac{1 \times 7 + 3}{7} = \frac{7+3}{7} = \frac{10}{7}$

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

Now we can rewrite the expression as:

$-\frac{4}{7} + \frac{10}{7} + \frac{9}{7}$

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

$\frac{-4 + 10 + 9}{7} = \frac{6 + 9}{7} = \frac{15}{7}$

We can leave it as an improper fraction or convert it back to a mixed number:

$\frac{15}{7} = \frac{14 + 1}{7} = \frac{14}{7} + \frac{1}{7} = 2 + \frac{1}{7} = 2\frac{1}{7}$

3. Final Answer

$\frac{15}{7}$ or $2\frac{1}{7}$