Answer :
To solve this problem, let's analyze the two conditions and the sets of [tex]\(x\)[/tex]-values provided. We need to determine which set of [tex]\(x\)[/tex]-values satisfies both conditions given:
1. [tex]\(0 \leq x \leq 7\)[/tex]
2. [tex]\(-7 \leq x \leq 7\)[/tex]
First Set of [tex]\(x\)[/tex]-values: [tex]\(-7, -2, 5, 7\)[/tex]
- Check each value against the first condition [tex]\(0 \leq x \leq 7\)[/tex]:
- [tex]\(-7\)[/tex] does not satisfy [tex]\(0 \leq x\)[/tex].
- [tex]\(-2\)[/tex] does not satisfy [tex]\(0 \leq x\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- Check each value against the second condition [tex]\(-7 \leq x \leq 7\)[/tex]:
- [tex]\(-7\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(-2\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
The first set does not satisfy the first condition for all values because [tex]\(-7\)[/tex] and [tex]\(-2\)[/tex] do not meet [tex]\(0 \leq x\)[/tex].
Second Set of [tex]\(x\)[/tex]-values: [tex]\(0, 2, 4, 5, 7\)[/tex]
- Check each value against the first condition [tex]\(0 \leq x \leq 7\)[/tex]:
- [tex]\(0\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(2\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(4\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- Check each value against the second condition [tex]\(-7 \leq x \leq 7\)[/tex]:
- [tex]\(0\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(2\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(4\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
The second set satisfies both conditions for all its values.
Therefore, the correct set of [tex]\(x\)[/tex]-values that satisfies both conditions is [tex]\([0, 2, 4, 5, 7]\)[/tex].
1. [tex]\(0 \leq x \leq 7\)[/tex]
2. [tex]\(-7 \leq x \leq 7\)[/tex]
First Set of [tex]\(x\)[/tex]-values: [tex]\(-7, -2, 5, 7\)[/tex]
- Check each value against the first condition [tex]\(0 \leq x \leq 7\)[/tex]:
- [tex]\(-7\)[/tex] does not satisfy [tex]\(0 \leq x\)[/tex].
- [tex]\(-2\)[/tex] does not satisfy [tex]\(0 \leq x\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- Check each value against the second condition [tex]\(-7 \leq x \leq 7\)[/tex]:
- [tex]\(-7\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(-2\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
The first set does not satisfy the first condition for all values because [tex]\(-7\)[/tex] and [tex]\(-2\)[/tex] do not meet [tex]\(0 \leq x\)[/tex].
Second Set of [tex]\(x\)[/tex]-values: [tex]\(0, 2, 4, 5, 7\)[/tex]
- Check each value against the first condition [tex]\(0 \leq x \leq 7\)[/tex]:
- [tex]\(0\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(2\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(4\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(0 \leq x \leq 7\)[/tex].
- Check each value against the second condition [tex]\(-7 \leq x \leq 7\)[/tex]:
- [tex]\(0\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(2\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(4\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(5\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
- [tex]\(7\)[/tex] satisfies [tex]\(-7 \leq x \leq 7\)[/tex].
The second set satisfies both conditions for all its values.
Therefore, the correct set of [tex]\(x\)[/tex]-values that satisfies both conditions is [tex]\([0, 2, 4, 5, 7]\)[/tex].
