Solve for Unknowns in the Equation: 46 - (98 + 3a) - (27b:3b/a - 7)

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

• Step 1: Simplify the expression inside the first parentheses: $98 + 3a$.
• Step 2: Simplify the expression inside the second parentheses, particularly the term $27b:\frac{3b}{a} - 7$.
• Step 3: Substitute simplified expressions back into the original expression.
• Step 4: Perform the necessary calculations to reach a simplified final expression.

Now, let's work through each step:

Step 1: Simplify $98 + 3a$. This remains as is within its parentheses.

Step 2: Simplify the term $27b:\frac{3b}{a} - 7$.

The fraction $27b:\frac{3b}{a} = 27b \times \frac{a}{3b} = 9a$ (assuming $b \neq 0$).
The expression inside becomes $9a - 7$.

Step 3: Substitute back:

The original expression is now:

$46 - (98 + 3a) - (9a - 7)$.

Step 4: Simplify:

First, distribute the subtraction across both terms inside their parentheses:

$46 - 98 - 3a - 9a + 7$.

Combine like terms by performing arithmetic operations:

$46 - 98 + 7 - 3a - 9a = (46 + 7 - 98) - (3a + 9a)$.

This simplifies to $-45 - 12a$.

Therefore, the solution to the problem is $-45-12a$.