Solve the following equations :
`3a-(1)/(5)=(a)/(5)+5(2)/(5)`

Answer

To solve the equation \( 3a - \frac{1}{5} = \frac{a}{5} + 5 \cdot \frac{2}{5} \), we will follow these steps:

### Step 1: Simplify the Right Side
First, we simplify the right side of the equation. The term \( 5 \cdot \frac{2}{5} \) simplifies to \( 2 \).

So, the equation becomes:
\[ 3a - \frac{1}{5} = \frac{a}{5} + 2 \]

### Step 2: Eliminate the Fractions
To eliminate the fractions, we can multiply every term in the equation by 5 (the least common multiple of the denominators).

Multiplying through by 5 gives:
\[ 5(3a) - 5\left(\frac{1}{5}\right) = 5\left(\frac{a}{5}\right) + 5(2) \]

This simplifies to:
\[ 15a - 1 = a + 10 \]

### Step 3: Rearrange the Equation
Next, we will rearrange the equation to group all terms involving \( a \) on one side and constant terms on the other side.

Subtract \( a \) from both sides:
\[ 15a - a - 1 = 10 \]

This simplifies to:
\[ 14a - 1 = 10 \]

### Step 4: Isolate \( a \)
Now, we will isolate \( a \) by adding 1 to both sides of the equation:
\[ 14a = 10 + 1 \]

This simplifies to:
\[ 14a = 11 \]

### Step 5: Solve for \( a \)
Finally, divide both sides by 14 to solve for \( a \):
\[ a = \frac{11}{14} \]

### Final Answer
Thus, the solution to the equation is:
\[ a = \frac{11}{14} \]

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