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.
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.