Solve the Algebraic Equation: 3a - (4c + 5a) Divided by 2/5a

To solve this problem, we'll follow these steps:

• Step 1: Simplify the division $(4c + 5a) \div \frac{2}{5a}$
• Step 2: Apply the simplified division to the subtraction $3a - X$
• Step 3: Simplify the expression obtained after subtraction

Now, let's work through each step in detail:

Step 1: Simplify the division $(4c + 5a) \div \frac{2}{5a}$.
When dividing by a fraction, we multiply by its reciprocal:

$(4c + 5a) \div \frac{2}{5a} = (4c + 5a) \times \frac{5a}{2}$

Distribute $\frac{5a}{2}$ to both terms inside the parentheses:

$4c \times \frac{5a}{2} + 5a \times \frac{5a}{2} = \frac{20ac}{2} + \frac{25a^2}{2} = 10ac + \frac{25}{2}a^2$

Step 2: Apply this result to the original subtraction:

$3a - (10ac + \frac{25}{2}a^2)$

Step 3: Combine all terms:

$3a - 10ac - \frac{25}{2}a^2$

Therefore, the simplified expression is:

$3a - 10ac - 12\frac{1}{2}a^2$