To solve the equation [tex]\(-3|x| = -6\)[/tex], follow these detailed steps:
1. Isolate the absolute value term:
[tex]\[
-3|x| = -6
\][/tex]
Divide both sides of the equation by -3 to get:
[tex]\[
|x| = \frac{-6}{-3}
\][/tex]
Simplify the right-hand side:
[tex]\[
|x| = 2
\][/tex]
2. Interpret the absolute value equation:
The absolute value equation [tex]\(|x| = 2\)[/tex] tells us that [tex]\(x\)[/tex] can be either the positive or negative value that results in 2 when its absolute value is taken.
Therefore, we have two cases to consider:
[tex]\[
x = 2 \quad \text{or} \quad x = -2
\][/tex]
3. Write down the solutions:
The two solutions to the equation are:
[tex]\[
x = 2, -2
\][/tex]
Hence, the solutions to the equation [tex]\(-3|x| = -6\)[/tex] are:
[tex]\[
x = 2, -2
\][/tex]
