To solve the problem of finding the set [tex]\(\{3x \mid x \in \mathbb{N}, 3 \leq x \leq 6\}\)[/tex], we will go through the given condition step by step.
1. Identify the range of [tex]\(x\)[/tex]: According to the problem, [tex]\(x\)[/tex] is a natural number ([tex]\(x \in \mathbb{N}\)[/tex]) and it must satisfy the condition [tex]\(3 \leq x \leq 6\)[/tex]. Therefore, [tex]\(x\)[/tex] can be one of the following values: [tex]\(3, 4, 5,\)[/tex] or [tex]\(6\)[/tex].
2. Apply the transformation [tex]\(3x\)[/tex] to each [tex]\(x\)[/tex]: We need to multiply each valid [tex]\(x\)[/tex] within the specified range by 3.
- When [tex]\(x = 3\)[/tex]:
[tex]\[
3 \times 3 = 9
\][/tex]
- When [tex]\(x = 4\)[/tex]:
[tex]\[
3 \times 4 = 12
\][/tex]
- When [tex]\(x = 5\)[/tex]:
[tex]\[
3 \times 5 = 15
\][/tex]
- When [tex]\(x = 6\)[/tex]:
[tex]\[
3 \times 6 = 18
\][/tex]
3. List the results: The results of these calculations are:
[tex]\[
9, 12, 15, 18
\][/tex]
4. Formulate the resulting set: We collected all the results from step 2 into a set. Hence, the set [tex]\(\{3x \mid x \in \mathbb{N}, 3 \leq x \leq 6\}\)[/tex] is:
[tex]\[
\{9, 12, 15, 18\}
\][/tex]
Therefore, the final result for the set [tex]\(\{3x \mid x \in \mathbb{N}, 3 \leq x \leq 6\}\)[/tex] is [tex]\(\{9, 12, 15, 18\}\)[/tex].
