To solve the equation [tex]\( 36 - 3|x| = 18 \)[/tex], we follow these steps:
1. Isolate the absolute value expression:
[tex]\[
36 - 3|x| = 18
\][/tex]
Subtract 36 from both sides to isolate [tex]\( -3|x| \)[/tex]:
[tex]\[
-3|x| = 18 - 36
\][/tex]
Simplify the right side:
[tex]\[
-3|x| = -18
\][/tex]
2. Divide both sides by -3:
[tex]\[
|x| = \frac{-18}{-3}
\][/tex]
Simplify the fraction:
[tex]\[
|x| = 6
\][/tex]
3. Consider the definition of the absolute value:
The equation [tex]\( |x| = 6 \)[/tex] means that [tex]\( x \)[/tex] can be 6 or -6. Therefore, we have two cases to consider:
[tex]\[
x = 6 \quad \text{or} \quad x = -6
\][/tex]
Thus, the solutions to the equation [tex]\( 36 - 3|x| = 18 \)[/tex] are:
[tex]\[
x = 6 \quad \text{and} \quad x = -6
\][/tex]
