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

Answer :

To solve the inequality [tex]\( x - 46 \geq -79 \)[/tex], we need to find the values of [tex]\( x \)[/tex] that satisfy this condition. Here's how you solve it step-by-step:

1. Start with the inequality:
[tex]\[
x - 46 \geq -79
\][/tex]

2. To isolate [tex]\( x \)[/tex], add 46 to both sides of the inequality:
[tex]\[
x - 46 + 46 \geq -79 + 46
\][/tex]
This simplifies to:
[tex]\[
x \geq -33
\][/tex]

Now, we need to check which values in the options satisfy the inequality [tex]\( x \geq -33 \)[/tex].

Let's look at each option:

- A. 14: Since 14 is greater than -33, it satisfies the inequality.
- B. -25: Since -25 is greater than -33, it satisfies the inequality.
- C. -33: Since -33 is equal to -33, it satisfies the inequality.
- D. 25: Since 25 is greater than -33, it satisfies the inequality.
- E. -45: Since -45 is less than -33, it does not satisfy the inequality.
- F. -39: Since -39 is less than -33, it does not satisfy the inequality.

Therefore, the elements of the solution set are: 14, -25, -33, and 25.

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