To solve the equation [tex]\( |x| - 8 = -5 \)[/tex], we need to follow these steps:
1. Isolate the absolute value term:
To do this, add 8 to both sides of the equation:
[tex]\[
|x| - 8 + 8 = -5 + 8 \implies |x| = 3
\][/tex]
2. Understand the absolute value equation:
The equation [tex]\( |x| = 3 \)[/tex] tells us that [tex]\( x \)[/tex] can be any number whose absolute value is 3. This gives us two possible solutions because the absolute value of both positive and negative numbers of the same magnitude is the same.
[tex]\[
x = 3 \quad \text{or} \quad x = -3
\][/tex]
3. List the possible solutions:
The solutions to the equation [tex]\( |x| = 3 \)[/tex] are
[tex]\[
x = 3 \quad \text{and} \quad x = -3
\][/tex]
4. Match the solutions to the multiple-choice options:
- Option 1: [tex]\( x = -13 \)[/tex] and [tex]\( x = -3 \)[/tex]
- Option 2: [tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex]
- Option 3: [tex]\( x = 3 \)[/tex] and [tex]\( x = 13 \)[/tex]
- Option 4: No solution
Comparing our solutions ([tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex]) with the options given, we see that Option 2 lists the correct solutions: [tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex].
Therefore, the correct answer is:
\boxed{2}
