To solve the equation [tex]\( |x+3| = 12 \)[/tex], we need to consider two separate cases because the absolute value operation can yield two different equations: one for the positive scenario and one for the negative scenario.
Case 1: [tex]\( x+3 = 12 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x + 3 = 12 \\
x = 12 - 3 \\
x = 9
\][/tex]
Case 2: [tex]\( x+3 = -12 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x + 3 = -12 \\
x = -12 - 3 \\
x = -15
\][/tex]
So, the solutions to the equation [tex]\( |x+3| = 12 \)[/tex] are [tex]\( x = 9 \)[/tex] and [tex]\( x = -15 \)[/tex].
Hence, the correct answer is:
D. [tex]\( x = 9, -15 \)[/tex]
