Question

Which values from this set {−12, −9, −3, 0, 3, 6} satisfy this inequality: −1/3x + 3 ≥ 6?

Option 1: 9, −3, 0, 3, and 6 only
Option 2: 0, 3, and 6 only
Option 3: −12, −9, and −3 only
Option 4: −12 and −9 only

Answer 1

To find which values satisfy the inequality −1/3x + 3 ≥ 6, we solve the inequality and find x ≤ −9. The values −12 and −9 from the provided set satisfy this condition.

Step-by-step explanation:

The student wants to determine which values from the set {−12, −9, −3, 0, 3, 6} satisfy the inequality −1/3x + 3 ≥ 6. We solve this inequality step by step:

1. First, subtract 3 from both sides to isolate the term involving x: −1/3x ≥ 6 − 3.
2. This simplifies to −1/3x ≥ 3.
3. Next, to solve for x, multiply both sides by −3 (the reciprocal of −1/3): x ≤ −9.

Now, we compare this solution to the set and find the values that are less than or equal to −9, which are −12 and −9. Therefore, the correct option is: Option 4: −12 and −9 only.