To solve the equation [tex]\(-2|2.2x - 3.3| = -6.6\)[/tex], let's break it down step-by-step:
### Step 1: Isolate the absolute value expression
Given:
[tex]\[
-2|2.2x - 3.3| = -6.6
\][/tex]
First, divide both sides of the equation by [tex]\(-2\)[/tex]:
[tex]\[
|2.2x - 3.3| = 3.3
\][/tex]
### Step 2: Solve the absolute value equation
The equation [tex]\(|2.2x - 3.3| = 3.3\)[/tex] means that the expression [tex]\(2.2x - 3.3\)[/tex] can be either [tex]\(3.3\)[/tex] or [tex]\(-3.3\)[/tex]. We need to set up two separate equations to solve for [tex]\(x\)[/tex]:
#### Case 1: [tex]\(2.2x - 3.3 = 3.3\)[/tex]
Add [tex]\(3.3\)[/tex] to both sides:
[tex]\[
2.2x = 6.6
\][/tex]
Divide both sides by [tex]\(2.2\)[/tex]:
[tex]\[
x = \frac{6.6}{2.2} = 3
\][/tex]
#### Case 2: [tex]\(2.2x - 3.3 = -3.3\)[/tex]
Add [tex]\(3.3\)[/tex] to both sides:
[tex]\[
2.2x = 0
\][/tex]
Divide both sides by [tex]\(2.2\)[/tex]:
[tex]\[
x = \frac{0}{2.2} = 0
\][/tex]
### Step 3: Write the solutions
The solutions to the equation are [tex]\(x = 3\)[/tex] and [tex]\(x = 0\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{x = 0 \text{ or } x = 3}
\][/tex]
