Solve the Nested Equation: Find t in 78 - (95 - 2t:3x/4)

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

• Step 1: Simplify the expression inside the parentheses.
• Step 2: Simplify the entire expression.

Let's execute each step in detail:

Step 1:
The expression given is $78 - (95 - 2t:\frac{3x}{4})$.

First, rewrite $2t:\frac{3x}{4}$ as $2t \times \frac{4}{3x}$.

This results in $\frac{8t}{3x}$.

So, the expression becomes:

$78 - (95 - \frac{8t}{3x})$.

Simplify the expression inside the parentheses:

The expression $95 - \frac{8t}{3x}$ remains as is, with no common operations, except subtraction.

Now, evaluate the subtraction:

$78 - (95 - \frac{8t}{3x}) = 78 - 95 + \frac{8t}{3x}$.

Simplify the subtraction:

$78 - 95 = -17$.

So the expression can be further simplified as:

$-17 + \frac{8t}{3x}$.

Expressing $\frac{8t}{3x}$ as a mixed number, we obtain:

$\frac{8t}{3x} = 2\frac{2}{3}\frac{t}{x}$.

Therefore, the entire expression becomes:

$\frac{8}{3x}t - 17 = 2\frac{2}{3}\frac{t}{x} - 17$.

Thus, the simplified form of the original expression is $2\frac{2}{3}\frac{t}{x} - 17$.