We need to solve the following equation for $x$: $7.511 - [7.88 - (150.12 / x - 1.24)] / 0.48 = 1.011$

1. Problem Description

We need to solve the following equation for $x$:

$7.511 - [7.88 - (150.12 / x - 1.24)] / 0.48 = 1.011$

2. Solution Steps

First, let's isolate the term with the brackets:

$7.511 - [7.88 - (150.12 / x - 1.24)] / 0.48 = 1.011$

Subtract 7.511 from both sides:

$- [7.88 - (150.12 / x - 1.24)] / 0.48 = 1.011 - 7.511$

$- [7.88 - (150.12 / x - 1.24)] / 0.48 = -6.5$

Multiply both sides by -1:

$[7.88 - (150.12 / x - 1.24)] / 0.48 = 6.5$

Multiply both sides by 0.48:

$7.88 - (150.12 / x - 1.24) = 6.5 * 0.48$

$7.88 - (150.12 / x - 1.24) = 3.12$

Subtract 7.88 from both sides:

$- (150.12 / x - 1.24) = 3.12 - 7.88$

$- (150.12 / x - 1.24) = -4.76$

Multiply both sides by -1:

$150.12 / x - 1.24 = 4.76$

Add 1.24 to both sides:

$150.12 / x = 4.76 + 1.24$

$150.12 / x = 6$

Multiply both sides by $x$:

$150.12 = 6x$

Divide both sides by 6:

$x = 150.12 / 6$

$x = 25.02$

3. Final Answer

$x = 25.02$