Question

Which of the following values are solutions to the inequality 5, is less than or equal to, 5, minus, 6, x, question mark5≤5−6x?
I., 2, II., 6, III., 0
I.2II.6III.0
Answer
Multiple Choice Answers
NoneNone
I onlyI only
II onlyII only
III onlyIII only
I and III and II
I and IIII and III
II and IIIII and III
I, II and IIII, II and III

Answer 1

To determine which values solve the inequality \( 5 \leq 5 - 6x \), we first need to solve the inequality for \( x \).

1. **Set up the inequality:**
\[
5 \leq 5 - 6x
\]

2. **Subtract 5 from both sides:**
\[
0 \leq -6x
\]

3. **Divide by -6 (remember to flip the inequality sign):**
\[
0 \geq x \quad \text{or} \quad x \leq 0
\]

Now that we have \( x \leq 0 \), we need to check each of the values:

- **I. \( 2 \)**:
\[
2 \nleq 0 \quad \text{(not a solution)}
\]

- **II. \( 6 \)**:
\[
6 \nleq 0 \quad \text{(not a solution)}
\]

- **III. \( 0 \)**:
\[
0 \leq 0 \quad \text{(solution)}
\]

From the checks, the only value that satisfies the inequality \( 5 \leq 5 - 6x \) is \( III. 0 \).

Thus, the answer is:
**III only**.