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Which answers are elements of the solution set of the inequality? Check all that apply.

[tex]x - 46 \geq -79[/tex]

A. -33
B. 14
C. -39
D. -25
E. -45
F. 25

Answer :

To solve the inequality [tex]\(x - 46 \geq -79\)[/tex], follow these steps:

1. Isolate the variable [tex]\(x\)[/tex]:
Add 46 to both sides of the inequality to get rid of the -46:
[tex]\[
x - 46 + 46 \geq -79 + 46
\][/tex]
Simplifying this, you get:
[tex]\[
x \geq -33
\][/tex]

Now, we need to determine which of the provided choices -33, 14, -39, -25, -45, and 25 satisfy the inequality [tex]\(x \geq -33\)[/tex].

2. Evaluate each option:
- A. [tex]\(-33\)[/tex]: Since [tex]\(-33 \geq -33\)[/tex], this is true.
- B. [tex]\(14\)[/tex]: Since [tex]\(14 \geq -33\)[/tex], this is true.
- C. [tex]\(-39\)[/tex]: Since [tex]\(-39 \geq -33\)[/tex] is false, it does not satisfy the inequality.
- D. [tex]\(-25\)[/tex]: Since [tex]\(-25 \geq -33\)[/tex], this is true.
- E. [tex]\(-45\)[/tex]: Since [tex]\(-45 \geq -33\)[/tex] is false, it does not satisfy the inequality.
- F. [tex]\(25\)[/tex]: Since [tex]\(25 \geq -33\)[/tex], this is true.

Thus, the elements of the solution set that satisfy the inequality [tex]\(x \geq -33\)[/tex] are:

- [tex]\(-33\)[/tex]
- [tex]\(14\)[/tex]
- [tex]\(-25\)[/tex]
- [tex]\(25\)[/tex]

So, the correct answers are A, B, D, and F.

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