Question

Which choice best describes the solution set?




1≤x<−25

−1≤x<25

x≥1 or
x<−25

x≤−1or
x>25

Answer 1

12x-3 ≥ 15x or -0.2x +10 < 5

Answer 2

To describe the solution set among the given choices, let's analyze each option with respect to their boundaries:

1. **1 ≤ x < -25**: This set is impossible because there are no values of x that can simultaneously satisfy both conditions (it cannot be both greater than or equal to 1 and less than -25).

2. **−1 ≤ x < 25**: This set includes all values of x from -1 up to, but not including, 25.

3. **x ≥ 1 or x < -25**: This means x can either be greater than or equal to 1 or less than -25, which results in two separate intervals: [1, ∞) and (-∞, -25).

4. **x ≤ −1 or x > 25**: This means x can either be less than or equal to -1 or greater than 25. This also results in two separate intervals: (-∞, -1] and (25, ∞).

If we want to determine which of these descriptions best concisely captures the nature of a solution set, it depends on specific criteria that might pertain to the question you are exploring.

Without additional context about what the solution set should encompass (e.g., values of x, constraints, inequalities), the choice would depend on what is asked.

- If the focus is on the range of values that solution set can take, option 2 (−1 ≤ x < 25) presents a continuous interval.
- If specified to include multiple conditions, option 3 and 4 indicate separated intervals based on the inequalities given.

Ultimately, the context will help determine which set best describes the desired solution.

Answer 3

To solve the inequality \( 12x - 3 \geq 15x \) or \( -0.2x + 10 < 5 \), we'll handle each part separately.

### Solve \( 12x - 3 \geq 15x \)

1. **Rearrange the inequality**:
\[
12x - 15x \geq 3
\]
\[
-3x \geq 3
\]

2. **Divide both sides by -3** (remember to flip the inequality):
\[
x \leq -1
\]

### Solve \( -0.2x + 10 < 5 \)

1. **Rearrange the inequality**:
\[
-0.2x < 5 - 10
\]
\[
-0.2x < -5
\]

2. **Divide both sides by -0.2** (again, flip the inequality):
\[
x > 25
\]

### Combine the results

Now we combine the two inequalities:

1. From the first inequality, we have \( x \leq -1 \).
2. From the second inequality, we have \( x > 25 \).

### Conclusion

The solution set for the compound inequality \( 12x - 3 \geq 15x \) or \( -0.2x + 10 < 5 \) is:

- \( x \leq -1 \) or \( x > 25 \)

So, the final answer is:
\[
x \leq -1 \quad \text{or} \quad x > 25
\]