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Answer :
To solve the inequality [tex]\( x - 46 \geq -79 \)[/tex] and determine which of the given numbers are elements of the solution set, follow these steps:
1. Isolate [tex]\( x \)[/tex]:
- Start with the inequality: [tex]\( x - 46 \geq -79 \)[/tex].
- To isolate [tex]\( x \)[/tex], add 46 to both sides of the inequality:
[tex]\[
x - 46 + 46 \geq -79 + 46
\][/tex]
- Simplify the expression:
[tex]\[
x \geq -33
\][/tex]
This tells us that the solution for [tex]\( x \)[/tex] is any number that is greater than or equal to [tex]\(-33\)[/tex].
2. Check which answers satisfy [tex]\( x \geq -33 \)[/tex]:
- A. [tex]\(-33\)[/tex]
- Since [tex]\(-33\)[/tex] is equal to [tex]\(-33\)[/tex], it satisfies the inequality.
- B. [tex]\(-39\)[/tex]
- [tex]\(-39\)[/tex] is less than [tex]\(-33\)[/tex], so it does not satisfy the inequality.
- C. [tex]\(-25\)[/tex]
- [tex]\(-25\)[/tex] is greater than [tex]\(-33\)[/tex], so it satisfies the inequality.
- D. [tex]\(25\)[/tex]
- [tex]\(25\)[/tex] is greater than [tex]\(-33\)[/tex], so it satisfies the inequality.
- E. [tex]\(14\)[/tex]
- [tex]\(14\)[/tex] is greater than [tex]\(-33\)[/tex], so it satisfies the inequality.
- F. [tex]\(-45\)[/tex]
- [tex]\(-45\)[/tex] is less than [tex]\(-33\)[/tex], so it does not satisfy the inequality.
3. Conclusion:
- The numbers that are elements of the solution set are [tex]\(-33\)[/tex], [tex]\(-25\)[/tex], [tex]\(25\)[/tex], and [tex]\(14\)[/tex].
Therefore, the correct answers are A. [tex]\(-33\)[/tex], C. [tex]\(-25\)[/tex], D. [tex]\(25\)[/tex], and E. [tex]\(14\)[/tex].
1. Isolate [tex]\( x \)[/tex]:
- Start with the inequality: [tex]\( x - 46 \geq -79 \)[/tex].
- To isolate [tex]\( x \)[/tex], add 46 to both sides of the inequality:
[tex]\[
x - 46 + 46 \geq -79 + 46
\][/tex]
- Simplify the expression:
[tex]\[
x \geq -33
\][/tex]
This tells us that the solution for [tex]\( x \)[/tex] is any number that is greater than or equal to [tex]\(-33\)[/tex].
2. Check which answers satisfy [tex]\( x \geq -33 \)[/tex]:
- A. [tex]\(-33\)[/tex]
- Since [tex]\(-33\)[/tex] is equal to [tex]\(-33\)[/tex], it satisfies the inequality.
- B. [tex]\(-39\)[/tex]
- [tex]\(-39\)[/tex] is less than [tex]\(-33\)[/tex], so it does not satisfy the inequality.
- C. [tex]\(-25\)[/tex]
- [tex]\(-25\)[/tex] is greater than [tex]\(-33\)[/tex], so it satisfies the inequality.
- D. [tex]\(25\)[/tex]
- [tex]\(25\)[/tex] is greater than [tex]\(-33\)[/tex], so it satisfies the inequality.
- E. [tex]\(14\)[/tex]
- [tex]\(14\)[/tex] is greater than [tex]\(-33\)[/tex], so it satisfies the inequality.
- F. [tex]\(-45\)[/tex]
- [tex]\(-45\)[/tex] is less than [tex]\(-33\)[/tex], so it does not satisfy the inequality.
3. Conclusion:
- The numbers that are elements of the solution set are [tex]\(-33\)[/tex], [tex]\(-25\)[/tex], [tex]\(25\)[/tex], and [tex]\(14\)[/tex].
Therefore, the correct answers are A. [tex]\(-33\)[/tex], C. [tex]\(-25\)[/tex], D. [tex]\(25\)[/tex], and E. [tex]\(14\)[/tex].
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