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Select the correct set of [tex]$x$[/tex]-values based on the given constraints:

1. [tex]$0 \leq x \leq 7$[/tex]
2. [tex]$-7 \leq x \leq 7$[/tex]

A. The [tex]$x$[/tex]-values are [tex]$-7, -2, 5,$[/tex] and [tex]$7$[/tex].

B. The [tex]$x$[/tex]-values are [tex]$0, 2, 4, 5,$[/tex] and [tex]$7$[/tex].

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].

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