To determine the expression equivalent to:

$\frac{2}{5}x + (-2) + (-4) - \frac{1}{5}x$

Step 1: Combine like terms involving $x$

The terms with $x$ are:

$\frac{2}{5}x \text{ and } -\frac{1}{5}x$

Combine them:

$\frac{2}{5}x - \frac{1}{5}x = \frac{1}{5}x$

Step 2: Combine constant terms

The constants are:

$-2 \text{ and } -4$

Combine them:

$-2 + (-4) = -6$

Step 3: Final expression

Combine the simplified terms:

$\frac{1}{5}x - 6$

Step 4: Compare with answer choices

The correct answer is:

D. $\frac{1}{5}x - 6$

Do you need more explanation on any of the steps? Let me know!

Here are 5 related questions for practice:

1. Simplify $\frac{3}{4}x - \frac{1}{4}x + 2 - 5$.
2. Combine like terms: $2x + 5x - 7 + 4$.
3. Solve for $x$: $3x - 2 = 7$.
4. Simplify $\frac{4}{3}x + \frac{2}{3}x - 5$.
5. Combine $\frac{5}{6}y - \frac{2}{6}y + 3$.

Tip: Always group like terms (terms with variables and constants separately) for quick simplification.