Let's simplify the given expression step by step:

$2\left(\dfrac{1}{5}m - \dfrac{2}{5}\right) + \dfrac{3}{5}$

Step 1: Distribute the 2 across the terms inside the parentheses.

We multiply $2$ by both $\dfrac{1}{5}m$ and $\dfrac{2}{5}$:

$2 \cdot \dfrac{1}{5}m = \dfrac{2}{5}m$ $2 \cdot \dfrac{2}{5} = \dfrac{4}{5}$

Now, the expression becomes:

$\dfrac{2}{5}m - \dfrac{4}{5} + \dfrac{3}{5}$

Step 2: Combine like terms.

The constants $-\dfrac{4}{5}$ and $\dfrac{3}{5}$ are like terms, so we combine them:

$-\dfrac{4}{5} + \dfrac{3}{5} = -\dfrac{1}{5}$

Now, the simplified expression is:

$\dfrac{2}{5}m - \dfrac{1}{5}$

Final Answer:

The simplified form of the expression is:

$\dfrac{2}{5}m - \dfrac{1}{5}$

Would you like a more detailed explanation of any step or have any other questions?

Here are 5 related questions you might find helpful:

1. How do you factor out common terms from algebraic expressions?
2. Can you solve an equation if $\dfrac{2}{5}m - \dfrac{1}{5} = 0$?
3. How do you handle fractions when solving algebraic equations?
4. What are the general steps for simplifying expressions involving distribution?
5. How do you solve for a variable when fractions are involved?

Tip: When simplifying, always combine like terms (such as constants or variables) to make your expression as simple as possible.