Question

what is the solution to $-2|2.2x - 3.3| = -6.6$?
$x = -3$ or $x = 0$
$x = -3$
$x = 3$
$x = 0$ or $x = 3$

Explanation:

Step1: Divide both sides by -2

To isolate the absolute value expression, we divide both sides of the equation \(-2|2.2x - 3.3| = -6.6\) by \(-2\).

$$ \frac{-2|2.2x - 3.3|}{-2}=\frac{-6.6}{-2} $$

Simplifying both sides, we get \(|2.2x - 3.3| = 3.3\).

Step2: Set up two equations

The absolute value equation \(|A| = B\) (where \(B\geq0\)) is equivalent to \(A = B\) or \(A=-B\). So we set up two equations:

1. \(2.2x - 3.3 = 3.3\)
2. \(2.2x - 3.3=- 3.3\)

Step3: Solve the first equation

For the equation \(2.2x - 3.3 = 3.3\), we add \(3.3\) to both sides:

$$ 2.2x-3.3 + 3.3=3.3 + 3.3 $$

Simplifying gives \(2.2x=6.6\). Then we divide both sides by \(2.2\):

$$ x=\frac{6.6}{2.2} = 3 $$

Step4: Solve the second equation

For the equation \(2.2x - 3.3=-3.3\), we add \(3.3\) to both sides:

$$ 2.2x-3.3 + 3.3=-3.3 + 3.3 $$

Simplifying gives \(2.2x = 0\). Then we divide both sides by \(2.2\):

$$ x=\frac{0}{2.2}=0 $$

Answer:

\(x = 0\) or \(x = 3\) (the option: \(x = 0\) or \(x = 3\))