Answer :
To solve the inequality [tex]\(x - 46 \geq -79\)[/tex], follow these steps:
1. Isolate [tex]\(x\)[/tex]: To get [tex]\(x\)[/tex] by itself, you need to add 46 to both sides of the inequality.
[tex]\[
x - 46 + 46 \geq -79 + 46
\][/tex]
2. Simplify the inequality:
[tex]\[
x \geq -33
\][/tex]
Now, you need to check which given options satisfy this inequality [tex]\(x \geq -33\)[/tex]. Let's go through each option:
- A. [tex]\(-25\)[/tex]:
[tex]\[
-25 \geq -33 \quad \text{(True)}
\][/tex]
- B. [tex]\(-39\)[/tex]:
[tex]\[
-39 \geq -33 \quad \text{(False)}
\][/tex]
- C. [tex]\(-33\)[/tex]:
[tex]\[
-33 \geq -33 \quad \text{(True)}
\][/tex]
- D. [tex]\(-45\)[/tex]:
[tex]\[
-45 \geq -33 \quad \text{(False)}
\][/tex]
- E. [tex]\(14\)[/tex]:
[tex]\[
14 \geq -33 \quad \text{(True)}
\][/tex]
- F. [tex]\(25\)[/tex]:
[tex]\[
25 \geq -33 \quad \text{(True)}
\][/tex]
So, the elements of the solution set for the inequality [tex]\(x - 46 \geq -79\)[/tex] that satisfy the condition [tex]\(x \geq -33\)[/tex] are: A (-25), C (-33), E (14), and F (25).
1. Isolate [tex]\(x\)[/tex]: To get [tex]\(x\)[/tex] by itself, you need to add 46 to both sides of the inequality.
[tex]\[
x - 46 + 46 \geq -79 + 46
\][/tex]
2. Simplify the inequality:
[tex]\[
x \geq -33
\][/tex]
Now, you need to check which given options satisfy this inequality [tex]\(x \geq -33\)[/tex]. Let's go through each option:
- A. [tex]\(-25\)[/tex]:
[tex]\[
-25 \geq -33 \quad \text{(True)}
\][/tex]
- B. [tex]\(-39\)[/tex]:
[tex]\[
-39 \geq -33 \quad \text{(False)}
\][/tex]
- C. [tex]\(-33\)[/tex]:
[tex]\[
-33 \geq -33 \quad \text{(True)}
\][/tex]
- D. [tex]\(-45\)[/tex]:
[tex]\[
-45 \geq -33 \quad \text{(False)}
\][/tex]
- E. [tex]\(14\)[/tex]:
[tex]\[
14 \geq -33 \quad \text{(True)}
\][/tex]
- F. [tex]\(25\)[/tex]:
[tex]\[
25 \geq -33 \quad \text{(True)}
\][/tex]
So, the elements of the solution set for the inequality [tex]\(x - 46 \geq -79\)[/tex] that satisfy the condition [tex]\(x \geq -33\)[/tex] are: A (-25), C (-33), E (14), and F (25).
