Simplify the Algebraic Expression: Solve 49 + 2a - (54a + 9a ÷ (5a × 3))

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

• Step 1: Simplify the expression within the division $9a:(5a\cdot3)$.
• Step 2: Simplify the expression by performing the arithmetic operations.

Let's solve the problem step by step:
**Step 1**: Simplify $9a:(5a\cdot3)$.
First, compute the product in the denominator: $5a \cdot 3 = 15a$.
Now, perform the division: $9a \div 15a = \frac{9a}{15a} = \frac{9}{15} = \frac{3}{5}$, assuming $a \neq 0$.

**Step 2**: Substitute back into the original expression:
The expression becomes $49 + 2a - (54a + \frac{3}{5})$.
Now distribute the negative sign: $49 + 2a - 54a - \frac{3}{5}$ Combine like terms: $(49 - \frac{3}{5}) + (2a - 54a)$ Simplify: $48\frac{2}{5} - 52a$

Therefore, the solution to the problem is $48\frac{2}{5}-52a$.