We need to solve the equation $9.501 - [(101.25 + x - 2.94) + 2.36] + 0.52 = 1.001$ for $x$.

1. Problem Description

We need to solve the equation $9.501 - [(101.25 + x - 2.94) + 2.36] + 0.52 = 1.001$ for $x$.

2. Solution Steps

First, simplify the expression inside the brackets:

$101.25 - 2.94 + 2.36 = 100.67$.

So the equation becomes:

$9.501 - [100.67 + x] + 0.52 = 1.001$

$9.501 - 100.67 - x + 0.52 = 1.001$

$-x - 90.649 + 0.52 = 1.001$

$-x - 90.129 = 1.001$

$-x = 1.001 + 90.129$

$-x = 91.13$

$x = -91.13$

Now, we write the steps in more detail:

$9.501 - [(101.25 + x - 2.94) + 2.36] + 0.52 = 1.001$

$9.501 - [101.25 + x - 2.94 + 2.36] + 0.52 = 1.001$

$9.501 - [101.25 - 2.94 + 2.36 + x] + 0.52 = 1.001$

$9.501 - [100.67 + x] + 0.52 = 1.001$

$9.501 - 100.67 - x + 0.52 = 1.001$

$10.021 - 100.67 - x = 1.001$

$-90.649 - x = 1.001$

$-x = 1.001 + 90.649$

$-x = 91.65$

$x = -91.65$

3. Final Answer

$x = -91.65$