To solve for the set of possible values of [tex]\( m \)[/tex] given the equation [tex]\( 3m = n - 7 \)[/tex] and the set of possible values of [tex]\( n \)[/tex] as [tex]\(\{-2, 1, 4\}\)[/tex], we will follow a step-by-step approach.
1. Substitute [tex]\( n = -2 \)[/tex] into the equation [tex]\( 3m = n - 7 \)[/tex]:
[tex]\[
3m = -2 - 7
\][/tex]
Simplify the right-hand side:
[tex]\[
3m = -9
\][/tex]
Divide both sides by 3 to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{-9}{3} = -3
\][/tex]
2. Substitute [tex]\( n = 1 \)[/tex] into the equation [tex]\( 3m = n - 7 \)[/tex]:
[tex]\[
3m = 1 - 7
\][/tex]
Simplify the right-hand side:
[tex]\[
3m = -6
\][/tex]
Divide both sides by 3 to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{-6}{3} = -2
\][/tex]
3. Substitute [tex]\( n = 4 \)[/tex] into the equation [tex]\( 3m = n - 7 \)[/tex]:
[tex]\[
3m = 4 - 7
\][/tex]
Simplify the right-hand side:
[tex]\[
3m = -3
\][/tex]
Divide both sides by 3 to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{-3}{3} = -1
\][/tex]
So, the set of possible values of [tex]\( m \)[/tex] is [tex]\( \{-3, -2, -1\} \)[/tex].
Given the choices:
A. [tex]\(\{-27, -18, -9\}\)[/tex]
B. [tex]\(\{-9, -6, -3\}\)[/tex]
C. [tex]\(\{-6, -3, 0\}\)[/tex]
D. [tex]\(\{-3, -2, -1\}\)[/tex]
The correct answer is:
D. [tex]\(\{-3, -2, -1\}\)[/tex]
