To solve the compound inequality \( \frac{1}{5}x < -1 \) or \( 6x > 0 \), we'll solve each inequality separately and then combine the results.

### Solve \( \frac{1}{5}x < -1 \):
1. Multiply both sides by 5 to eliminate the fraction:
   \[
   x < -1 \times 5
   \]
2. Simplify:
   \[
   x < -5
   \]

### Solve \( 6x > 0 \):
1. Divide both sides by 6:
   \[
   x > 0
   \]

### Combine the results:
Since this is an "or" compound inequality, we combine the results:
- The solution to \( \frac{1}{5}x < -1 \) is \( x < -5 \).
- The solution to \( 6x > 0 \) is \( x > 0 \).

Thus, the solution is \( x < -5 \) or \( x > 0 \).

Would you like more details or have any questions about this solution? 

Here are some related questions:

1. What happens if the compound inequality is "and" instead of "or"?
2. How would you graph the solution on a number line?
3. What if \( \frac{1}{5}x \) was greater than -1 instead of less?
4. Can you have a solution that includes all real numbers?
5. How do you solve compound inequalities with more than two inequalities?

**Tip:** When dealing with compound inequalities, always remember to handle "and" and "or" separately, as they affect how you combine the solutions.

Learn how to solve compound inequalities 1/5x < -1 or 6x > 0 with a detailed step-by-step solution. This problem covers key algebraic concepts related to inequalities. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation